The number of unused states in a 4-bit Johnson counter is 8.

Explanation:
A Johnson counter is a type of shift register that cycles through a sequence of states. In a 4-bit Johnson counter, the counter has four flip-flops or stages, each representing one bit. The counter can cycle through a total of 2^4 = 16 states.

To determine the number of unused states, we need to consider the sequence of states that the counter cycles through. In a Johnson counter, the sequence of states is such that only one bit changes at a time, either going from 0 to 1 or from 1 to 0. This ensures that adjacent states in the sequence differ by only one bit.

Let's consider the binary representation of the states in a 4-bit Johnson counter:

0000
0001
0011
0111
1111
1110
1100
1000

From the above sequence, we can observe that there are 8 unused states. These are the states that are not included in the above sequence. The unused states are:

0100
0101
1010
1011
0100
0101
1010
1011

Therefore, the number of unused states in a 4-bit Johnson counter is 8.

In summary:
- A 4-bit Johnson counter has a total of 16 states.
- The sequence of states in a Johnson counter ensures that only one bit changes at a time.
- The unused states are the ones that are not included in the sequence of states.
- In a 4-bit Johnson counter, there are 8 unused states.