DESIGN PROBLEM : 4-bit increment by 2 circuit

Problem: Derive the logical expression for a 4-bit increment by 2 circuit and draw the architecture of it.

Solution: The task here is to design a circuit that increments its count by two. Since, it is a 4-bit circuit, the total number of possible states is 16. Each state transitions to the state which has a binary value two greater than it. Now, there are two possible scenarios based upon the initial state that the counter gets into:

1. It can count 0 -> 2 -> 4 -> 6 -> 8 -> 10 -> 12 -> 14 -> 0 (their binary equivalents)

2. It can count 1 -> 3 -> 5 -> 7 -> 9 -> 11 -> 13 -> 15 -> 1 (their binary equivalents)

The state transition table can be represented as shown below:

We can find the expression for outputs using K-maps as below.

Expression for D3(next): Let us first derive the expression for D3(next). The K-map can be represented as below:

The expression for D3(next) as derived from K-map is:

D3(next) = D3.D2' + D3.D1' + D3'.D2.D1

D3(next) = D3.(D2'+D1') + D3'.D2.D1.

D3(next) = D3.(D2.D1)'+D3'.(D2.D1)

D3(next) = D3 (exor) (D2.D1) 

Expression for D2(next): Given below is the K-map derived from state transition table for D2(next).

The expression for D2(next) as derived from K-map is:

D2(next) = D2'.D1 + D2.D1' = D2 (exor) D1

Expression for D1(next):  Given below is the K-map derived from state transition table for D1(next).

The expression for D1(next) is derived from K-map as:

D1(next) = D1'

Expression for D0(next): Given below is the K-map for D0(next).

The expression for D0(next) is:

D0(next) = D0

Combining all the expressions, the circuit is as given below:

Can you come up with a better solution for this problem? Let us know your views in comments.

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