Three T flip flops are connected to form a counter. The maximum states...
To understand why the maximum states possible for the counter formed by three T flip flops is 8, let's break it down step by step.
T flip flops are a type of flip flop that toggle its output based on the input signal. Each T flip flop has one input (T) and two outputs (Q and Q'). The Q output represents the current state of the flip flop, while the Q' output represents the complement of the Q output.
A counter is a sequential circuit that counts the number of events or cycles. In this case, we are using T flip flops to build the counter. Each T flip flop represents one bit of the counter, and the number of states the counter can have is determined by the number of bits.
In a binary system, the number of states for n bits is 2^n. Therefore, for a counter formed by three T flip flops, the number of states can be calculated as 2^3 = 8.
To understand why it is 8, let's look at the binary representation of the states:
- State 0: Q2 Q1 Q0 = 000
- State 1: Q2 Q1 Q0 = 001
- State 2: Q2 Q1 Q0 = 010
- State 3: Q2 Q1 Q0 = 011
- State 4: Q2 Q1 Q0 = 100
- State 5: Q2 Q1 Q0 = 101
- State 6: Q2 Q1 Q0 = 110
- State 7: Q2 Q1 Q0 = 111
As you can see, with three T flip flops, we can represent 8 different states. The counter will cycle through these states in a specific sequence determined by the clock signal and the inputs to the T flip flops.
Therefore, the correct answer is option C) 8.
Three T flip flops are connected to form a counter. The maximum states...
Concept:
For a counter with ‘n’ flip flops:
- The total number of states = 2n (0 to 2n – 1)
- The largest number that can be stored in the counter = 2n – 1
To construct a counter with any MOD number, the minimum number flip flops required must satisfy:
Modulus ≤ 2n
Where n is the number of flip-flops and is the minimum value satisfying the above condition.
Calculation:
The total number of states required when n = 3:
23 ≥ 8
The states will vary from (0 to 7)
So the maximum states possible for the counter will be 8.