Question

In a 4-bit ring counter, the number of used states are and the number of unused states are

• A. 4 and 8
• B. 4 and 4
• C. 4 and 12
• D. 2 and 12

Hint:

To distinguish between counters: - Ring Counter: Used states = $n$. - Johnson Counter: Used states = $2n$. - Binary Counter: Used states = $2^n$.

Answer 1

The Correct Option is C

A ring counter is a circular shift register where the output of the last flip-flop is connected back to the input of the first flip-flop. 1. Total Possible States: For any digital circuit with $n$ flip-flops, the total number of mathematically possible binary states is $2^n$. For a 4-bit counter ($n=4$): $$\text{Total States} = 2^4 = 16$$

2. Used States in a Ring Counter: A ring counter is unique because it only uses one "1" (or one "0") that circulates through the stages. In an $n$-bit ring counter, the number of valid or "used" states is exactly equal to the number of flip-flops ($n$).

• Used States (4-bit): 4 (specifically: 1000, 0100, 0010, 0001)

3. Calculating Unused States: Unused states are the states that the counter never enters during normal operation. These are calculated by subtracting the used states from the total possible states: $$\text{Unused States} = \text{Total States} - \text{Used States}$$ $$\text{Unused States} = 16 - 4 = 12$$ Therefore, in a 4-bit ring counter, there are 4 used states and 12 unused states.