Past exam of the year 1 of the computer science course of the University of Oxford / 2003 / Functional programming, data structures and algorithms, procedural programming, and digital hardware / 9 / d / Solution

Let $(L^{+},G^{+})$ denote the state after the next active clock edge. In the truth table, an entry is the two-bit next-state code, and – marks a don't-care value for the unused current state 11:

For each input column, 01 forces $L^{+}{G}^{+}=10$, 10 forces $01$, and the two equal-input columns copy the current code. Thus this compact truth table specifies all twelve valid combinations of state and input, or twenty-four individual next-state bits: