Active low clock transitions from low to high. A clock having a small circle (bubble) in the input side would count clock transitions from high to low. This the concept of active low ---that is, an action occurs when the input is low.
As an example of how this circuit might be used, suppose that the counter consists of four flip-flops, all of which are RESET. That is, the binary number stored in the counter is 0000.The clock signal is initially held low, Now the clock is allowed to ‘’run’’ for six clock periods, and then it is held low, as shown in Fig. 1-21b. After the first clock transition from low to high, the counter will advance to 0001. After the second transition, it will advance to 0010, and so on, until it will store the binary number 0110. After the sixth transition. The binary number 0110 is equal 6, and thus the counter has counted and stored the six clock transitions! The waveform in Fig. 1-21b shows the clock with the counter contents directly beneath each transition
Maximum count =2^n -1
Where n = number of flip-flops
The term 2^n means 2 raised to the nth power, that is, 2 multiplied by itself n times. For example
〖 2〗^2=2*2=4
〖 2〗^3=2*2*2=8
〖 2〗^4=2*2*2*2=16
〖 2〗^5=2*2*2*2*2=32
〖 2〗^6=2*2*2*2*2*2=64
〖 2〗^7=128
〖 2〗^8=256
〖 2〗^9=512
〖 2〗^10=1024
We’ll spend more time on binary and decimal numbers in Chapter 5. For now this listing of powers of 2 can be used with Eq. (1-1). For example, the four-flip-flop counter has a maximum decimal count of
Maximum count = 2^4 - 1 = 16 – 1 = 15
EXAMPLE 1-2
What is the maximum decimal count for a counter composed of eight flip-flops?
SOLUTION
Using Eq. (1-1)
Maximum count = 2^8 – 1 = 256 – 1 = 255