Past exam of the year 1 of the computer science course of the University of Oxford / 2016 / Digital systems, linear algebra, introduction to formal proof (resit) / 2 / c

Address a read-only memory with the two state bits and two input bits. Each word stores the two next-state bits and INC, so a direct replacement for all the combinational logic is $16\times 3$ bits, or 48 bits. Program its 16 words from the state table, duplicating a state's output over all four input addresses. The two D flip-flops and clock remain outside the ROM.

If INC retains its separate two-state-bit decoder, only the next-state logic needs a $16\times 2$-bit ROM, plus that output gate. Storing output in a separate state-only ROM would use $4\times 1$ further bits. These factored options have a different boundary from replacing all the combinational logic with one ROM.