Memory systems and operation methods thereof, memory controllers and memories

A memory controller, the memory controller to be coupled to a memory, the memory including a memory cell array and a peripheral circuit coupled to the memory cell array, the memory cell array including memory cells capable of storing m bits of information, wherein m is a positive integer greater than 1, wherein the memory cell array stores data in at least a first writing state, and wherein the memory controller configured to at least:

• send a prefix command and n groups of page data to the peripheral circuit to cause the peripheral circuit to generate a (n+1)th group of page data according to the prefix command and the n groups of page data, wherein n is a positive integer and n+1 is a positive integer less than or equal to m, wherein the n groups of page data include lower page data, middle page data, upper page data, and extra page data, wherein the prefix command is to include a logic operation to generate the (n+1)th group of page data based on a second writing state, wherein the second writing state is selected based on a function of the memory, and wherein the second writing state stores data in less data states than the first writing state;
• generate 2n different data states in the memory cell array, wherein a memory cell of the memory cell array includes a data state of the 2n different data states;
• and
• cause writing of the n groups of page data and the (n+1)th group of page data based on the second writing state into the memory cell of the memory cell array.

A memory comprising:

• a memory cell array including memory cells capable of storing m bits of information;
• a peripheral circuit coupled to the memory cell array, wherein the memory cell array stores data in at least a first writing state, and wherein the peripheral circuit is configured to:
• receive a prefix command and n groups of page data, wherein n is a positive integer, and n+1 is a positive integer less than or equal to m, wherein the received prefix command corresponds to a command to store data in a second writing state, and wherein the second writing state is selected based on a function of the memory;
• generate a (n+1)th group of page data based on the received prefix command and the n groups of page data, wherein the n groups of page data include lower page data, middle page data, upper page data, and extra page data, wherein the received prefix command includes a logic operation to generate the (n+1)th group of page data based on the second writing state, and wherein the second writing state stores data in less data states than the first writing state;
• and
• write the n groups of page data and the (n+1)th group of page data based on the second writing state into a memory cell of the memory cell array to generate 2n different data states in the memory cell array, wherein the memory cell of the memory cell array includes a data state of the 2n different data states.