Question

can someone help me with the following :(

implement a digital circuit that allows you to obtain the comparison results for a pair of four-bit numbers, when they are equal, one greater than the other and vice versa

Answer 1

Solution:-

4 bit magnitude comparator: The given logic has a two 4-bit numbers and the magnitude is compared. Let the two 4 bit numbers be A, B. The two numbers are compared bit by bit using Ex-nor gates and there will be three outputs: A=B, A>B and A<B. The 4 bit inputs are A: ​​​​​​, B:

As it compares the magnitude and gives the result, it is known as 4 bit magnitude comparator.

Boolean expression using logic:-

We obtain the logic for three outputs step by step by comparison of each bit and obtain boolean expression as follows :-

A=B: The output must be high when all the 4 bits of A and B must be same. That means when the output must be HIGH. So, we use EX NOR gate for equality and AND gate to satisfy the logic.

A>B: The condition to satisfy A>B is possible for the four cases mentioned below:-

1. A3 = 1,B3 = 0

2. A3=B3 and A2 = 1, B2 = 0

3. A3 = B3 and A2 = B2 and A1 = 1, B1 = 0

4. A3 = B3 and A2 =B2 and A1 = B1 and A0 = 1, B0 = 0

A<B: The condition to satisfy A<B is possible for the four cases mentioned below:-

1. A3 = 0, B3 = 1

2. A3 = B3 and A2 = 0, B2 = 1

3. A3 = B3 and A2 = B2 and A1 = 0, B1 = 1

4. A3 = B3 and A2 = B2 and A1 = B1 and A0 = 0,B0 = 1

The below boolean expression uses the combination of EX NOR and AND, OR gates to implement the logics for the three outputs mentioned above.

The circuit logic diagram is drawn for three outputs from the above derived boolean logic equation.

Hence obtained the logic circuit and boolean expression that satisfies the given specifications.