Question

We need to design a logic circuit for interchanging two logic signals. The system has three inputs I1I1, I2I2, and SS as well as two outputs O1 and O2. When S is low, we should have O1 = I1 and O2 = I2. On the other hand, when S is high,we should have O1 = I2 and O2 =I1. Thus, S acts as the control input for a reversing switch. Use Karnaugh maps to obtain a minimal SOP(sum ofproduct) design. Draw the circuit.

Answer 1

Explanation:

Inputs and Outputs:

There are 3 inputs = I₁, I₂, and S

There are 2 outputs = O₁ and O₂

The given problem is solved in three major steps:

Step 1: Construct the Truth Table

Step 2: Obtain the logic equations using Karnaugh map

Step 3: Draw the logic circuit

Step 1: Construct the Truth Table

The given logic is

When S = 0 then O₁ = I₁ and O₂ = I₂

When S = 1 then O₁ = I₂ and O₂ = I₁

I₁     |     I₂     |    S    |    O₁    |    O₂

0     |     0     |    0    |    0    |     0

0     |     0     |    1     |    0    |     0

0     |     1      |    0    |    0    |     1

0     |     1      |    1     |    1     |     0

1      |     0     |    0    |    1     |     0

1      |     0     |    1     |    0    |     1

1      |     1      |    0    |    1     |     1

1      |     1      |    1     |    1     |     1

Step 2: Obtain the logic equations using Karnaugh map

Please refer to the attached diagram where Karnaugh map is set up.

The minimal SOP representation for output O₁

$O_1 = I_1 \bar{S} + I_2 S$

The minimal SOP representation for output O₂

$O_2 = I_2 \bar{S} + I_1 S$

Step 3: Draw the logic circuit

Please refer to the attached diagram where the circuit has been drawn.