Digital Teaching Aid 
Counter  Lesson 8 
Lesson Plan 

To understand how this counter works lets have a look at the timing diagram:
The frequency of waveform C is one half that at B, but is only oneeighth the clock frequency.
The FF's are negative edge triggered, hence output signals change only at the falling side of the clock pulse.
Fig. 83: Truth table, asynchronous mod 8 counter
CLK transition 
C 
B 
A 
0 
0 
0 
0 
1 
0 
0 
1 
2 
0 
1 
0 
3 
0 
1 
1 
4 
1 
0 
0 
5 
1 
0 
1 
6 
1 
1 
0 
7 
1 
1 
1 
0 
0 
0 
0 
A three FlipFlop counter is often referred to as a mod 8 (modulus 8) counter since it has 8 states.
2^{3} = 8 output conditions 
(The exponent equals to the number of FlipFlops) 
The largest decimal number which is represented by a 3 FlipFlop counter is:

2^{3}  1 = 7 
In general: 
2^{n}  1 
Count Down mode
Switching the clock inputs of each FlipFlop to the _{}
HO: How many FlipFlops are required to construct a mod128 counter? A mod32? What is the largest decimal number that can be stored in a mod64 counter?
Solution:
* mod128 must have 7 FlipFlops (27 = 128)
* mod32 must have 5 FlipFlops
* mod64, the largest decimal number is 63