Method of operation of arithmetic and logic unit, storage medium, and arithmetic and logic unit

A method of operation of an arithmetic and logic unit for transforming

• all problems for which a model can be created by a serial structure of decisions having an order dependency configured by
• having N (N is any positive integer) number of decision nodes having dependency input/outputs each executing a predetermined decision based on a single or a plurality of data inputs comprising an R-nary number or quantity of logical value information and a dependency input comprising binary information indicating "valid" or "invalid" at a point of time when both of the data input and the dependency input become valid and each outputting a conclusion output comprising an R-nary number or quantity of logical value information and a dependency output comprising binary information indicating "valid" or "invalid" and
• having a relationship of relative order between the decision nodes having dependency input/outputs, having the dependency input of the decision node having a dependency input/output of the most significant bit always being "valid", and having the dependency output of a decision node having a dependency input/output located at a higher significant bit connected as the dependency input of a decision node having a dependency input/output located at one lower significant bit from that decision node having a dependency input/output to
• a binary tree structure having N number of decision nodes not having dependency input/outputs for each executing a predetermined decision based on a single or a plurality of data inputs comprising an R-nary number or a quantity of logical value information at a point of time when the data input becomes valid and outputting a code of a format combining into one an indeterminate code "Q" of the meaning "cannot be defined" and a quantity as a working conclusion and
• defining the N number of decision nodes not having dependency input/outputs as leaves,
• said method of operation of an arithmetic and logic unit replacing a decision node having a dependency input/output by
• a decision node not having a dependency input/output having a connotation decision node for executing a predetermined decision based on a single or a plurality of data inputs comprising an R-nary number or quantity of logical value information and a dependency input always comprising "valid" at a point of time when the data input becomes valid and outputting a conclusion output comprising an R-nary number or quantity of logical value information and a dependency output comprising binary information indicating "valid" or "invalid" and an indeterminate code generation node for outputting an indeterminate code "Q" when the dependency output of the connotation decision node becomes "valid" and outputting a code of a format combining in one the indeterminate code "Q" and the quantity as the working conclusion of the decision node not having a dependency input/output.

A method of operation of an arithmetic and logic unit for transforming

• all problems for which a model can be created by a serial structure of decisions having an order dependency configured by
• having N (N is any positive integer) number of decision nodes having dependency input/outputs for each executing a predetermined decision based on a single or a plurality of data inputs comprising an R-nary number or quantity of logical value information and a dependency input comprising binary information indicating "valid" or "invalid" at a point of time when both of the data input and the dependency input become valid and each outputting a conclusion output comprising an R-nary number or quantity of logical value information and a dependency output comprising binary information indicating "valid" or "invalid" and
• having a relationship of relative order between the decision nodes having dependency input/outputs, having the dependency input of the decision node having a dependency input/output of the most significant bit always being "valid", and having the dependency output of a decision node having a dependency input/output located at a higher significant bit connected as the dependency input of a decision node having a dependency input/output located at one lower significant bit from that decision node having a dependency input/output to
• a binary tree structure having N number of decision nodes not having dependency input/outputs for each executing a predetermined decision based on a single or a plurality of data inputs comprising an R-nary number or quantity of logical value information at a point of time when the data input becomes valid and outputting a code of a format combining into one an indeterminate code "Q" of the meaning "cannot be defined" and the quantity as a working conclusion and
• higher priority determination nodes, corresponding to the series of decisions, which each receives as its input the working conclusions of two decision nodes not having dependency input/outputs or the working conclusions of two higher priority determination nodes in front of this higher priority determination node and outputs the working conclusion of the decision node not having a dependency input/output of a higher significant bit or the working conclusion of the higher priority determination node of a higher significant bit as the working conclusion of that higher priority determination node when the working conclusion of the decision node not having a dependency input/output of a higher significant bit or the working conclusion of the higher priority determination node of a higher significant bit is not the indeterminate code "Q", while outputs the working conclusion of the decision node not having a dependency input/output of a lower significant bit or the working conclusion of the higher priority determination node of a lower significant bit as the working conclusion of that higher priority determination node when the working conclusion of the decision node not having a dependency input/output of a higher significant bit or the working conclusion of the higher priority determination node of a higher significant bit is the indeterminate code "Q" and
• defining the decision nodes not having dependency input/outputs as leaves and defining the higher priority determination nodes as other nodes other than leaves,
• said method of operation of an arithmetic and logic unit replacing a decision node having a dependency input/output by
• a decision node not having a dependency input/output having a connotation decision node for executing a predetermined decision based on a single or a plurality of data inputs comprising an R-nary number or quantity of logical value information and a dependency input always comprising "valid" at a point of time when the data input becomes valid and outputting a conclusion output comprising an R-nary number or quantity of logical value information and a dependency output comprising binary information indicating "valid" or "invalid" and an indeterminate code generation node for outputting an indeterminate code "Q" when the dependency output of the connotation decision node becomes "valid" and outputting a code of a format combining in one the indeterminate code "Q" and the quantity as the working conclusion of the decision node not having a dependency input/output.

A method of operation of an arithmetic and logic unit for realizing a priority encoding function for outputting as a binary number, with respect to data input of n-bit binary numbers, a bit position which is first "1" or "0" in a direction from the most significant bit to the least significant bit or the number of continuous "1's" or "0's" in the direction from the most significant bit to the least significant bit by creating a model by a binary tree defining a processing for a decision not having a dependency input/output as a leaf and defining processing for determination of a higher priority as another node other than a leaf,

• in said method of operation of an arithmetic and logic unit,
• the processings for decisions not having dependency input/outputs, corresponding to each bit of the data input, each executing a predetermined decision based on one bit of the data input at the point of time when the data input becomes valid and outputting a code of a format combining into one an indeterminate code "Q" indicating "cannot be defined" and a quantity as a working conclusion;
• the processings for determination of higher priorities, corresponding to each bit of the data input, each receiving as its input the working conclusions of two processings for decisions not having dependency input/outputs or the working conclusions of two processings for determination of higher priorities in front of the same, outputting the working conclusion of the processing for a decision not having a dependency input/output of a higher significant bit or the working conclusion of the processing for determination of a higher priority of a higher significant bit as the working conclusion when the working conclusion of the processing for a decision not having significant dependency input/output of a higher significant bit or the working conclusion of the processing for determination of a higher priority of a higher significant bit is not the indeterminate code "Q", and outputting the working conclusion of the processing for a decision not having a dependency input/output of a lower significant bit or the working conclusion of the processing for determination of a higher priority of a lower significant bit as the working conclusion when the working conclusion of the processing for a decision not having a dependency input/output of a higher significant bit or the working conclusion of the processing for determination of a higher priority of a higher significant bit is the indeterminate code "Q";
• and
• all processings for decisions serving as leaves of the binary tree and all processings for determination of higher priorities located at the same depth in the binary tree being respectively processed in parallel and the working conclusion of the higher priority determination node serving as a root of the binary tree being defined as the conclusion of the priority encoding.

A method of operation of an arithmetic and logic unit for solving a problem including a series of decisions having an order dependency by creating a model by a binary tree defining processings for decisions, corresponding to the decisions, as leaves and defining processings for determination of higher priorities as other nodes other than leaves,

• in said method of operation of an arithmetic and logic unit, the processings for decisions outputting any one of "true", "false", and "neither true nor false or do not know" as a result of decision based on one or a plurality of input information;
• the processings for determination of higher priorities, corresponding to the series of decisions, each receiving as its input the results of decisions of two processings for decisions or the results of decisions of two processings for determination of higher priorities in front of the same, outputting the result of decision of the processing for a decision of the higher significant bit or the processing for determination of a higher priority of the higher significant bit when the result of decision of the processing for a decision of the higher significant bit or the processing for determination of a higher priority of the higher significant bit is "true" or "false", and outputting the result of decision of the processing for a decision of the lower significant bit or the processing for determination of a higher priority of the lower significant bit when the result of decision of the processing for a decision of the higher significant bit or the processing for determination of a higher priority of the higher significant bit is "neither true nor false or do not know";
• and
• all processings for decisions serving as leaves of the binary tree and all processings for determination of higher priorities located at the same depth in the binary tree being respectively processed in parallel.

A method of operation of an arithmetic and logic unit for finding the absolute value of the difference of two numbers (X, Y) of n number of digits of any R-nary number by creating a model by one column of n number of processings for decisions, all filled by n number of binary trees defining the processings for decisions from the first digit to a g-th digit (g=1 to n) as the leaves and defining other nodes other than the leaves as the processings for determination of higher priorities, and a matrix comprising n number of rows and m number of columns (m is the smallest integer exceeding log.sub.2 n) of processings for determination of higher priorities

• in said method of operation of an arithmetic and logic unit, the processings for decisions each outputting as the result of decision a value code "Y" meaning "true" when the result of the difference (X-Y) of two numbers of the same digit place becomes negative, outputting a value code "N" meaning "false" when the result becomes positive, and outputting a value code "Q" meaning "neither true nor false or do not know" when the result becomes zero;
• the processings for determination of higher priorities, corresponding to the series of decisions, each receiving as its input the results of decisions of two processings for decisions or the results of decisions of two processings for determination of higher priorities in front of the same, outputting the result of decision of the processing for a decision of the higher significant bit or the processing for determination of a higher priority of the higher significant bit when the result of decision of the processing for a decision of the higher significant bit or the processing for determination of a higher priority of the higher significant bit is "true" or "false", and outputting the result of decision of the processing for a decision of a lower significant bit or the processing for determination of a higher priority of the lower significant bit when the result of decision of the processing for a decision of the higher significant bit or processing for determination of a higher priority of the higher significant bit is "neither true nor false or do not know";
• and
• the one column of n number of processings for decisions and the constituent elements of the columns comprising the matrix comprising the n number of rows and m number of columns of processings for determination of higher priorities being respectively simultaneously processed and a borrow operation of each digit being generated from each processing for determination of a higher priority of the m-th column.

An arithmetic and logic unit for solving a problem including a series of decisions having an order dependency, said arithmetic and logic unit having

• decision nodes not having dependency input/outputs, corresponding to the decisions, for each executing a predetermined decision based on a single or a plurality of data inputs comprising an R-nary number or quantity of logical value information at a point of time when the data input becomes valid and outputting a code of a format combining in one an indeterminate code "Q" indicating "cannot be defined" and the quantity as a working conclusion and
• higher priority determination nodes, corresponding to the series of decisions, for each receiving as its input the working conclusions of two decision nodes not having dependency input/outputs or the working conclusions of two higher priority determination nodes in front of the same, outputting the working conclusion of the decision node not having a dependency input/output of the higher significant bit or the working conclusion of the higher priority determination node of the higher significant bit as the working conclusion when the working conclusion of the decision node not having the dependency input/output of the higher significant bit or the working conclusion of the higher priority determination node of the higher significant bit is not the indeterminate code "Q", and outputting the working conclusion of the decision node not having a dependency input/output of the lower significant bit or the working conclusion of the higher priority determination node of the lower significant bit as the working conclusion when the working conclusion of the decision node not having a dependency input/output of the higher significant bit or the working conclusion of the higher priority determination node of the higher significant bit is the indeterminate code "Q" and
• creating a model for the problem by a binary tree defining a decision node not having a dependency input/output as a leaf and defining a higher priority determination node as another node other than a leaf, simultaneously processing all decision nodes serving as the leaves and all higher priority determination nodes located at the same depth in the binary tree, and defining the working conclusion of the higher priority determination node serving as a root of the binary tree as the conclusion of the problem.

An arithmetic and logic unit configured to transform a serial structure of decisions having an order dependency configured by

• having N (N is any positive integer) number of decision nodes having dependency input/outputs for each executing a predetermined decision based on a single or a plurality of data inputs comprising an R-nary number or quantity of logical value information and a dependency input comprising binary information indicating "valid" or "invalid" at a point of time when both of the data input and the dependency input become valid and outputting a conclusion output comprising an R-nary number or quantity of logical value information and a dependency output comprising the binary information indicating "valid" or "invalid", and
• having a relationship of relative order between the decision nodes having dependency input/outputs, having the dependency input of the decision node having a dependency input/output of the most significant bit always being "valid", and having the dependency output of a decision node having a dependency input/output located at a higher significant bit connected as the dependency input of a decision node having a dependency input/output located at one lower significant bit from that decision node having a dependency input/output to
• a binary tree structure having N number of decision nodes not having dependency input/outputs for each executing a predetermined decision based on a single or a plurality of data inputs comprising an R-nary number or quantity of logical value information at a point of time when the data input becomes valid and outputting a code of a format combining in one an indeterminate code "Q" indicating "cannot be defined" and the quantity as the working conclusion and
• defining the N number of decision nodes not having dependency input/outputs as leaves,
• said arithmetic and logic unit replacing a decision node having a dependency input/output by
• a decision node not having a dependency input/output having a connotation decision node for executing a predetermined decision based on a single or a plurality of data inputs comprising an R-nary number or quantity of logical value information and a dependency input always comprising "valid" at a point of time when the data input becomes valid and outputting a conclusion output comprising an R-nary number or quantity of logical value information and a dependency output comprising binary information indicating "valid" or "invalid" and an indeterminate code generation node for outputting an indeterminate code "Q" when the dependency output of the connotation decision node becomes "valid" and outputting a code of a format combining in one the indeterminate code "Q" and the quantity as the working conclusion.

An arithmetic and logic unit configured to transform a serial structure of decisions having an order dependency configured by

• having N (N is any positive integer) number of decision nodes having dependency input/outputs for each executing a predetermined decision based on a single or a plurality of data inputs comprising an R-nary number or quantity of logical value information and a dependency input comprising binary information indicating "valid" or "invalid" at a point of time when both of the data input and the dependency input become valid and outputting a conclusion output comprising an R-nary number or quantity of logical value information and a dependency output comprising the binary information indicating "valid" or "invalid", and
• having a relationship of relative order between the decision nodes having dependency input/outputs, having the dependency input of the decision node having a dependency input/output of the most significant bit always being "valid", and having the dependency output of a decision node having a dependency input/output located at a higher significant bit connected as the dependency input of a decision node having a dependency input/output located at one lower significant bit from that decision node having a dependency input/output to
• a binary tree structure having N number of decision nodes not having dependency input/outputs for each executing a predetermined decision based on a single or a plurality of data inputs comprising an R-nary number or quantity of logical value information at a point of time when the data input becomes valid and outputting a code of a format combining into one an indeterminate code "Q" of the meaning "cannot be defined" and the quantity as a working conclusion and
• higher priority determination nodes, corresponding to the series of decisions, which each receives as its input the working conclusions of two decision nodes not having dependency input/outputs or the working conclusions of two higher priority determination nodes in front of this higher priority determination node and outputs the working conclusion of the decision node not having a dependency input/output of a higher significant bit or the working conclusion of the higher priority determination node of a higher significant bit as the working conclusion of that higher priority determination node when the working conclusion of the decision node not having a dependency input/output of a higher significant bit or the working conclusion of the higher priority determination node of a higher significant bit is not the indeterminate code "Q", while outputs the working conclusion of the decision node not having a dependency input/output of a lower significant bit or the working conclusion of the higher priority determination node of a lower significant bit as the working conclusion of that higher priority determination node when the working conclusion of the decision node not having a dependency input/output of a higher significant bit or the working conclusion of the higher priority determination node of a higher significant bit is the indeterminate code "Q" and
• defining the decision nodes not having dependency input/outputs as leaves and defining the higher priority determination nodes as other nodes other than leaves,
• said arithmetic and logic unit replacing a decision node having a dependency input/output by
• a decision node not having a dependency input/output having a connotation decision node for executing a predetermined decision based on a single or a plurality of data inputs comprising an R-nary number or quantity of logical value information and a dependency input always comprising "valid" at a point of time when the data input becomes valid and outputting a conclusion output comprising an R-nary number or quantity of logical value information and a dependency output comprising binary information indicating "valid" or "invalid" and an indeterminate code generation node for outputting an indeterminate code "Q" when the dependency output of the connotation decision node becomes "valid" and outputting a code of a format combining in one the indeterminate code "Q" and the quantity as the working conclusion.

An arithmetic and logic unit provided with a priority encoding function for outputting as a binary number, with respect to data input of n-bit binary numbers, a bit position which is first "1" or "0" in a direction from the most significant bit to the least significant bit,

• said arithmetic and logic unit having
• decision nodes not having dependency input/outputs, corresponding to each bit of the data input, each executing a predetermined decision based on one bit of the data input at the point of time when the data input becomes valid and outputting a code of a format combining into one an indeterminate code "Q" indicating "cannot be defined" and a quantity as a working conclusion and
• higher priority determination nodes, corresponding to each bit of the data input, each receiving as its input the working conclusions of two decision nodes not having dependency input/outputs or the working conclusions of two higher priority determination nodes in front of the same, outputting the working conclusion of the decision node not having a dependency input/output of a higher significant bit or the working conclusion of the higher priority determination node of a higher significant bit as the working conclusion when the working conclusion of the decision node not having significant dependency input/output of a higher significant bit or the working conclusion of the higher priority determination node of a higher significant bit is not the indeterminate code "Q", and outputting the working conclusion of the decision node not having a dependency input/output of a lower significant bit or the working conclusion of the higher priority determination node of a lower significant bit as the working conclusion when the working conclusion of the decision node not having a dependency input/output of a higher significant bit or the working conclusion of the higher priority determination node of a higher significant bit is the indeterminate code "Q" and
• creating a model of the priority encoding function by a binary tree defining a decision node not having a dependency input/output as a leaf and defining a higher priority determination node as another node other than a leaf, simultaneously processing all decision nodes serving as leaves and all higher priority determination nodes located at the same depth in the binary tree, and defining the working conclusion of the higher priority determination node serving as a root of the binary tree as the conclusion of the priority encoding function.

An arithmetic and logic unit provided with a priority encoding function for outputting as a binary number, with respect to a data input of n-bit binary numbers, a bit position which is first "1" or "0" in a direction from the most significant bit to the least significant bit,

• in said arithmetic and logic unit, a model is created for said arithmetic and logic unit by a binary tree of a height m (m is the smallest integer exceeding log.sub.2 n),
• the binary tree has Nm (Nm is the smallest integer exceeding n/2) number of nodes of a depth m and Ns (Ns is the smallest integer exceeding Ns+1/2) number of nodes of a depth s (s is an integer represented as s=1 to m-1);
• the pm-th (pm=1 to Nm) nodes from the least significant bit of the depth m of the binary tree
• each uses a (2.times.pm-2)-th bit signal line and a (2.times.pm-1)-th bit signal line of the data input as the zero-th bit input and the first bit input and
• has an OR logic means for taking the OR logic of the zero-th bit input and the first bit input and outputting the result as the first bit output and
• a connection line for outputting the first bit input as the zero-th bit output;
• the ps-th (ps=1 to Ns) nodes from the least significant bit of the depth s of the binary tree
• each uses the zero-th bit output to the (m-s)-th bit output of a (2.times.ps-1)-th node of the depth (s+1) of the binary tree as the zero-th bit input to the (m-s)-th bit input of a lower significant bit and uses the zero-th bit output to the (m-s)-th bit output of a (2.times.ps)-th node of the depth (s+1) of the binary tree as the zero-th bit input to the (m-s)-th bit input of a higher significant bit and
• has an OR logic means for taking the OR logic of the (m-s)-th bit input of the lower significant bit and the (m-s)-th bit input of the higher significant bit and outputting the result as an (m-s+1)-th bit output,
• a connection line for outputting the (m-s)-th bit input of the higher significant bit as the (m-s)-th bit output, and
• (m-s+1) number of selecting means;
• and
• a q-th (q=1 to m-s+1)-th selecting means from the least significant bit receives as its input the (m-s)-th bit of the higher significant bit as the selection input, selects the (q-1)-th bit input of the higher significant bit when the selection input is "true", selects the (q-1)-th bit input of the lower significant bit when the selection input is "false", and outputs the result as the (q-1)-th bit output.

An arithmetic and logic unit provided with a priority encoding function for outputting as a binary number, with respect to data input of n-bit binary numbers, the number of continuous "1's" or "0's" in the direction from the most significant bit to the least significant bit,

• said arithmetic and logic unit having
• decision nodes not having dependency input/outputs, corresponding to the individual bits of the data input, for each executing a predetermined decision based on one bit of the data input at a point of time when the data input becomes valid and outputting a code of a format combining in one an indeterminate code "Q" of the meaning "cannot be defined" and a quantity as a working conclusion and
• higher priority determination nodes, corresponding to the individual bits of the data input, which each receives as its input the working conclusions of two decision nodes not having dependency input/outputs or working conclusions of two higher priority determination nodes in front of the same, outputs the working conclusion of the decision node not having a dependency input/output of the higher significant bit or the working conclusion of the higher priority determination node of the higher significant bit as the working conclusion when the working conclusion of the decision node not having a dependency input/output of the higher significant bit or the working conclusion of the higher priority determination node of the higher significant bit is not the indeterminate code "Q", and outputs the working conclusion of the decision node not having a dependency input/output of the lower significant bit or the working conclusion of the higher priority determination node of the lower significant bit as the working conclusion when the working conclusion of the decision node not having a dependency input/output of the higher significant bit or the working conclusion of the higher priority determination node of the higher significant bit is the indeterminate code "Q";
• and
• the priority encoding function is realized by creating a model by a binary tree using decision nodes not having dependency input/outputs as leaves and using higher priority determination nodes as nodes other than the leaves, simultaneously processing all decision nodes serving as leaves and all higher priority determination nodes located at the same depth in the binary tree, and using the working conclusion of the higher priority determination node serving as the root of the binary tree as the conclusion of the priority encoding function.

An arithmetic and logic unit provided with a priority encoding function for outputting as a binary number, with respect to data input of n-bit binary numbers, the number of continuous "1's" or "0's" in the direction from the most significant bit to the least significant bit, wherein

• the arithmetic and logic unit is realized by creating of model by a binary tree of the height m (m is the smallest integer exceeding log.sub.2 n);
• the binary tree has Nm (Nm is the smallest integer exceeding n/2) number of nodes of the depth m and Ns (Ns is the smallest integer exceeding Ns+1/2) number of nodes of the depth s (s is an integer represented as s=1 to m-1);
• the pm-th (pm=1 to Nm) nodes from the least significant bit of the depth m of the binary tree
• each uses a (2.times.pm-2)-th bit signal line and a (2.times.pm-1)-th bit signal line of the data input as the zero-th bit input and the first bit input and
• has an OR logic means for taking the OR logic of the zero-th bit input and the first bit input and outputting the result as the first bit output and
• a negative logic means for taking the negative logic of the first bit input and outputting this as the zero-th bit output;
• the ps-th (ps=1 to Ns) nodes from the least significant bit of the depth s of the binary tree
• each uses the zero-th bit output to the (m-s)-th bit output of the (2.times.ps-1)-th node of the depth (s+1) of the binary tree as the zero-th bit input to the (m-s)-th bit input of the lower significant bit and uses the zero-th bit output to the (m-s)-th bit output of the (2.times.ps)-th node of the depth (s+1) of the binary tree as the zero-th bit input to the (m-s)-th bit input of the higher significant bit and
• has an OR logic means for taking the OR logic of the (m-s)-th bit input of the lower significant bit and the (m-s)-th bit input of the higher significant bit and outputting the result as an (m-s+1)-th bit output,
• a negative logic means for taking the negative logic of the (m-s)-th bit input of the higher significant bit and outputting this as the (m-s)-th bit output, and
• (m-s+1) number of selecting means;
• and
• a q-th (q=1 to m-s+1)-th selecting means from the least significant bit receives as its input the (m-s)-th bit of the higher significant bit as the selection input, selects the (q-1)-th bit input of the higher significant bit when the selection input is "true", selects the(q-1)-th bit input of the lower significant bit when the selection input is "false", and outputs the same as the (q-1)-th bit output.

An arithmetic and logic unit for solving a problem including a series of decisions having an order dependency, having

• decision nodes, corresponding to the decisions, for each outputting either of "true", "false", and "neither true nor false or do not know" as the result of the decision based on one or a plurality of input information and
• higher priority determination nodes, corresponding to series of the decisions, for each receiving as its input the results of the decisions of two decision nodes or the results of the decisions of two higher priority determination nodes, outputs the result of the decision of the decision node of the higher significant bit or the higher priority determination node of the higher significant bit when the result of the decision of the decision node of the higher significant bit or the higher priority determination node of the higher significant bit is "true" or "false", and outputs the result of the decision of the decision node of the lower significant bit or the higher priority determination node of the lower significant bit when the result of the decision of the decision node of the higher significant bit or the higher priority determination node of the higher significant bit is "neither true nor false or do not know";
• and
• creating a model of the problem by a binary tree using decision nodes as leaves and higher priority determination nodes as nodes other than the leaves and simultaneously processing all decision nodes which serve as leaves and all higher priority determination nodes located at the same depth in the binary tree.

An arithmetic and logic unit wherein,

• when decisions of existence of a carry for the digits (Xai, Ybi;
• i=0 to n-1) of two numbers in the addition of two n-bit binary numbers (Xa, Yb) form a series of decisions having an order dependency,
• has n number of decision nodes which respectively output "true or false" when the result of the sum of the same digit places becomes 2 or more, "false or true" when the result becomes zero, and "neither true nor false or do not know" when the result becomes 1 as the results of the decisions based on the digit values Xai, Ybi of the two numbers and
• a higher priority determination node matrix comprising n number of rows and m number of columns (m is the smallest integer exceeding log.sub.2 n) with rows corresponding to the digits of the two numbers;
• the group of the higher priority determination nodes of the first column has
• a higher priority determination node of the zero-th row as a dummy node for propagating the result of decision of the decision node of the zero-th digit as it is and
• a higher priority determination node of an h1-th row which receives as its input the result of decision of an h1-1-th digit and the decision node of the h1--th digit (h1=1 to n-1), outputs the result of decision of the decision node of the h1-th digit when the result of decision of the decision node of the h1-th digit is "true" or "false", and outputs the result of decision of the decision node of the h1-1-th digit when the result of decision of the decision node of h1-th digit is "neither true nor false or do not know";
• the group of higher priority determination nodes of a k-th column (k=2 to m) has
• higher priority determination nodes from the zero-th row to a 2.sup.k-1 -th row as the dummy nodes for respectively propagating the result of decisions of the higher priority determination nodes from the zero-th row to the 2.sup.k-1 -th row as they are and
• a higher priority determination node of an hk-th row which receives as its input the results of decisions of the higher priority determination node of an hk-2.sup.k-1 -th row and the higher priority determination node of the hk-th row (hk=2.sup.k-1 to n-1), outputs the result of decision of the higher priority determination node of the hk-th row when the result of decision of the higher priority determination node of the hk-th row is "true" or "false", and outputs the result of decision of the higher priority determination node of the hk-2.sup.k-1 -th row when the result of decision of the higher priority determination node of the hk-th row is "neither true nor false or do not know";
• and
• the n number of decision nodes and the groups of higher priority determination nodes of the columns are respectively simultaneously processed.

An arithmetic and logic unit wherein,

• when the decisions of existence of a carry for the digits (Xai, Ybi;
• i=0 to n-1) of two numbers in the addition of two n-bit binary numbers (Xa, Yb) form a series of decisions having an order dependency,
• it has n number of decision nodes which respectively output "true or false" when the result of the sum of the same digit places becomes 2 or more, "false or true" when the result becomes zero, and "neither true nor false or do not know" when the result becomes 1 as the result of a decision based on the digit values Xai, Ybi of the two numbers and
• a higher priority determination node matrix consisting of n/2 number of rows and m number of columns (m is the smallest integer exceeding log.sub.2 n) with rows corresponding to the odd number digits of the two numbers;
• the group of higher priority determination nodes of the first column has
• a higher priority determination node of the h1-th row which receives as its input the results of the decisions of the h1-1-th digit and the decision node of h1-th digit (h1=odd number from 1 to n-1), outputs the result of decision of the decision node h1-th digit when the result of the decision of the decision node of the h1-th digit is "true" or "false", and outputs the result of the decision of the decision node of h1-1-th digit when the result of decision of the decision node of the h1-th digit is "neither true nor false or do not know";
• the group of higher priority determination nodes of the k-th column (k=2 to m) has
• higher priority determination nodes from the first to 2.sup.k-1 -th odd number rows as the dummy nodes for respectively propagating the results of decisions of the higher priority determination nodes from the first to 2.sup.k-1 -1-th odd number rows as they are and
• a higher priority determination node of the hk-th row which receives as its input the result of decision of the higher priority determination node of the hk-2.sup.k-1 -th row and the higher priority determination node of the hk-th row (hk=odd number from 2.sup.k-1 to n-1), outputs the result of decision of the higher priority determination node of the hk-th row when the result of decision of the higher priority determination node of the hk-th row is "true" or "false", and outputs the result of decision of the higher priority determination node of the hk-2.sup.k-1 -th row when the result of decision of the higher priority determination node of the hk-th row is "neither true nor false or do not know";
• and
• the n number of decision nodes and the groups of the higher priority determination nodes of the columns are respectively simultaneously processed.

An arithmetic and logic unit as set forth in claim 66, wherein:

• when the decisions of existence of a borrow for digits (Xai, Ybi;
• i=0 to n-1) of two numbers in the subtraction (Xa-Yb) of two n-bit binary numbers form a series of decisions having an order dependency,
• each decision node has
• an exclusive OR logic means for taking the exclusive OR logic of the digit value Xai and the digit value Ybi and outputting the result as the code Ti,1 and
• a connecting means for outputting the digit value Ybi as the code Ti,0.

An arithmetic and logic unit, wherein,

• when the decisions of existence of a borrow for the digits (Xai, Ybi;
• i=0 to n-1) in the subtraction (Xa-Yb) of two n-bit binary numbers form a series of decisions having an order dependency,
• it has n number of decision nodes which respectively output "true or false" when the result of the difference of two numbers of the same digit places becomes negative, "false or true" when the result becomes positive, and "neither true nor false or do not know" when the result becomes zero as a result of the decision based on the digit values Xai, Ybi of the two numbers and
• a higher priority determination node matrix consisting of n number of rows and m number of columns (m is the smallest integer exceeding log.sub.2 n) with rows corresponding to the digits of the two numbers;
• the group of higher priority determination nodes of the first column has
• a higher priority determination node of the zero-th row as a dummy node for propagating the result of decision of the decision node of the zero-th digit as it is and
• a higher priority determination node of the h1-th row which receives as its input the results of decisions of the h1-1-th digit and the decision node of h1-th digit (h1=1 to n-1), outputs the result of decision of the decision node of the h1-th digit as the result when the result of decision of the decision node of the h1-th digit is "true" or "false", and outputs the result of decision of the decision node of h1-1-th digit as the result when the result of decision of the decision node of h1-th digit is "neither true nor false or do not know";
• the group of higher priority determination nodes of the k-th column (k=2 to m) has
• higher priority determination nodes from the zero-th row to the 2.sup.k-1 -th row as the dummy nodes for respectively propagating the result of decisions of the higher priority determination nodes from the zero-th row to the 2.sup.k-1 -th row as they are and
• a higher priority determination node of the hk-th row which receives as its input the results of decisions of the higher priority determination node of the hk-2.sup.k-1 -th row and the higher priority determination node of the hk-th row (hk=2.sup.k-1 to n-1), outputs the result of the decision of the higher priority determination node of the hk-th row as the result when the result of the decision of the higher priority determination node of the hk-th row is "true" or "false", and outputs the result of the decision of the higher priority determination node of the hk-2.sup.k-1 -th row as the result when the result of the decision of the higher priority determination node of the hk-th row is "neither true nor false or do not know";
• and
• the n number of decision nodes and the groups of the higher significant priority determination nodes of the columns are respectively simultaneously processed.

An arithmetic and logic unit, wherein,

• when decisions of existence of a borrow for the digits (Xai Ybi;
• i=0 to n-1) in the subtraction of two n-bit binary numbers (Xa-Yb) forms a series of decisions having an order dependency,
• it has n number of decision nodes which respectively output "true or false" when the result of difference of two numbers of the same digit places becomes negative, "false or true" when the result becomes positive, and "neither true nor false or do not know" when the result becomes zero as the result of the decision based on the digit values Xai, Ybi of the two numbers and
• a higher priority determination node matrix comprising n/2 number of rows and m number of columns (m is the smallest integer exceeding log.sub.2 n) with rows corresponding to the odd number digits of the two numbers;
• the group of higher priority determination node of the first column has
• a higher priority determination node of the h1-th row which receives as its input the result of decision of the h1-1-th digit and the decision node of h1-th digit (h1=odd number from 1 to n-1), outputs the result of the decision of the decision node h1-th digit as the result when the result of decision of the decision node of the h1-th digit is "true" or "false", and outputs the result of the decision of the decision node of h1-1-th digit as the result when the result of decision of the decision node of h1-th digit is "neither true nor false or do not know";
• the group of higher priority determination nodes of the k-th column (k=2 to m) has
• higher priority determination nodes from the first to 2.sup.k-1 -th odd number rows as dummy nodes for respectively propagating the results of decisions of the higher priority determination nodes of the first to 2.sup.k-1 -1-th odd number rows as they are and
• a higher priority determination node of the hk-th row which receives as its input the result of decision of the higher priority determination node of the hk-2.sup.k-1 -th row and the higher priority determination node of the hk-th row (hk=odd number from 2.sup.k-1 to n-1), outputs the result of decision of the higher priority determination node of the hk-th row as the result when the result of decision of the higher priority determination node of the hk-th row is "true" or "false", and outputs the result of decision of the higher priority determination node of the hk-2.sup.k-1 -th row as the result when the result of decision of the higher priority determination node of the hk-th row is "neither true nor false or do not know";
• and
• the n number of decision nodes and the groups of the higher priority determination nodes of the columns are respectively simultaneously processed.

An arithmetic and logic unit for finding the absolute value of the difference of two n-bit binary numbers (Xa, Yb), having

• a decision node which outputs the value code "Y" meaning "true" when the result of difference (Xai-Ybi) of two numbers of the same digit places becomes negative, the value code "N" meaning "false" when the result becomes positive, and the value code "Q" meaning "neither true nor false or do not know" when the result becomes zero as the result of the decision based on the digit values Xai and Ybi (i=0 to n-1) of the two numbers and has
• a matrix of the higher priority determination nodes consisting of n number of rows and m number of columns (m is the smallest integer exceeding log.sub.2 n) with rows corresponding to the digits of the two numbers and
• a borrow generating unit for generating a borrow of the digits in the absolute value operation of the difference;
• the group of higher priority determination nodes of the first column has
• a higher priority determination node of the zero-th row as a dummy node for propagating the result of decision of the decision node of the zero-th digit as it is and
• a higher priority determination node of the h1-th row which receives as its input the result of decision of the h1-1-th digit and the decision node of h1-th digit (h1=1 to n-1), outputs the result of decision of the decision node of the h1-th digit as the result when the result of decision of the decision node of the h1-th digit is "true" or "false", and outputs the result of decision of the decision node of h1-1-th digit as the result when the result of decision of the decision node of h1-th digit is "neither true nor false or do not know";
• the group of higher priority determination nodes of the k-th column (k=2 to m) has
• higher priority determination nodes from the zero-th row to the 2.sup.k-1 -th row as the dummy nodes for respectively propagating the results of decisions of the higher priority determination nodes from the zero-th row to the 2.sup.k-1 -1-th row as they are and
• a higher priority determination node of the hk-th row which receives as its input the result of decision of the higher priority determination node of the hk-2.sup.k-1 -th row and the higher priority determination node of the hk-th row (hk=2.sup.k-1 to n-1), outputs the result of decision of the higher priority determination node of the hk-th row as the result when the result of decision of the higher priority determination node of the hk-th row is "true" or "false", and outputs the result of decision of the higher priority determination node of the hk-2.sup.k-1 -th row as the result when the result of decision of the higher priority determination node of the hk-th row is "neither true nor false or do not know";
• the borrow generation unit has
• a code judging means for judging the code for the result of difference (Xa-Yb) of the two numbers based on the result of the borrow generation of the n-1-th digit generated from the higher priority determination node of the n-1-th row and the m-th column,
• code replacing means from the zero-th row to the n-2-th row for replacing the value code "Q" with the value code "Q", the value code "Y" with the value code "N", and the value code "N"with the value code "Y", respectively for the output codes of the higher priority determination nodes from the zero-th row to the n-2-th row not including the higher priority determination node of the n-1-th row in the higher priority determination node group of the m-th column where the code is negative or negative or zero as the result of code judgement of the code judging means, respectively, and not performing the replacement, and leaving them as they are where the result is positive or zero or positive, and
• a second code replacing means of the zero-th row to the n-2-th row for replacing the value code "Q" with the value code "N" to obtain a borrow of each digit for the output of the code replacing means of the zero-th row to the n-2-th row;
• and
• the n number of decision nodes, the groups of higher priority determination nodes of the columns, and the code replacing means of the zero-th row to the n-2-th row and the second code replacing means are respectively simultaneously processed.