Synchronous binary counters are arguably the simplest sequential synchronous circuits. They use the flip-flops to store the circuit's count state and (usually) have no external inputs. Thus the next state (count) is determined solely by the last state (count). We again initially take an intuitive look at mod-N counters.
The waveforms required form mod-8 counter were shown in Fig. 7.1, being the outputs, fi2, Q, and Q〇t from the three flip-flops, If this synchronous mod-8 counter is to be built from negative edge triggered T-type flip-flops, then since all three flip-flops will be clocked together (as this is to be a synchronous circuit) we need to determine for each clock input whether the T input for each flip-flop must be 0 (for the output to remain the same) or 1 (for it to toggle).
By inspection of the waveforms in Fig. 7.1 it is clear that:
• Q0 must toggle on every negative edge of the system clock and so we need T0= 1; 〜
• Q1 must only toggle when Q0 = 1, and so we need T1= Q0；
• Q2 must only toggle when Q0 = 2, = 1 and so we need T2=Q0 * Q1
We must therefore use an AND gate to produce the steering logic (as it is known) to enable the toggling action of the flip-flops as required. The circuit f〇r the mod-8 synchronous counter is shown in Fig. 7.3.
From the above analysis of the required steering logic a clear pattern emerges of how to produce any mod-2n counter (where n is the number of flip-flops used). This is that the T input of each flip-flop must be the outputs from all preceding flip-flops AND’d together.