how many flip flops are required to count 8 clock pulses why?
Answers
Answer:
n flip-flops can represent 2n states. The number of bits needed to represent all the states will be the number of flip-flops needed to implement that state machine. So for this state diagram, 4 flip-flops are needed because one of the states is 1001, which needs 4 bits.
Answer:
Assuming you are asking about the minimum number of flip-flops required, the answer is either three or four flip-flops, depending on (a) the architecture of the flip flops, and (b) the initial state from which you begin counting.
If you configure individual flip-flops as a simple binary counter, and the initial state of the counter is 000, then you’d need
log 8 to the base 2 = 3
flip-flops to count from state 000 to states 001 (1), 010 (2), 011 (3), 100 (4), 101 (5), 110 (6), 111 (7). You’d need a fourth flip-flop to detect the eighth clock pulse, which would cause the counter to transition from state 1110 to state 1111 (8). Obviously with this counter configuration, you could continue to count up to the fifteenth clock pulse at state 1111 (15). However, in some triple flip flop integrated circuits (IC) binary counters, you are provided with what’s known as an overflow bit, which detects the transition from state 111 to the reset state of 000. In this case could start with an initial state of 000 and get by with only three flip-flops.
That said, if you had three individual flip-flops configured as a binary counter), you could count eight clock pulses without an overflow bit, if you set the initial state to 111 rather than 000. In that case the state sequence would be 111 (0), 000 (1), 001 (2), 010 (3), 011 (4), 100 (5), 101 (6), 110 (7), 111 (8).
In general, an N-bit counter has
possible states. However, if you’re using it to count clock pulses, and the initial state of the counter is all zeroes, and the counter lacks an overflow bit, you need one additional flip-flop to detect the Nth clock pulse.
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