Page 80 - DCAP108_DIGITAL_CIRCUITS_AND_LOGIC_DESIGNS

Unit 4: Minimization of Boolean Algebra

• K-map squares: These are labelled so that horizontally adjacent squares differ only in one Notes
variable and similarly, vertically adjacent squares differ only in one variable.
• Looping: The expression for output X can be simplified by properly combining those squares
in the ‘K-map which contain 1s. The process for combining these 1s is called looping.
• Maxterm: It is the sum of N distinct literals where each literal occurs exactly once.

• Minterm: It is the product of N distinct literals where each literal occurs exactly once.
• OR gate: It is used to perform the logical addition also known as OR gate. An OR gate has
two or more input signals and only one output signal.
• Quad: It is looped, the resultant term will contain only the variables do-not-change form
for all the squares in the quad.
• Redundant group: A group of 1s on a Karnaugh map that are all part of other groups. You
can eliminate any redundant group.

1. Prepare a Karnaugh map’s truth table three values.

2. Write an equation of SOP minimization technique and solve it.

4.6 Review Questions

1. Explain the 6-variable K-map and give the example with circuit diagram.
2. Explain the 4-variable K-map and give the example.

3. What is the sum-of-products circuits for the truth table given below?

A B C D Y
0 0 0 0 0
0 0 0 1 1
0 0 1 0 0
0 0 1 1 0
0 1 0 0 0
0 1 0 1 1
0 1 1 1 0
1 0 1 0 0
1 0 0 1 0
1 0 1 0 1
1 0 1 1 1
1 1 0 0 1
1 1 0 1 1
1 1 1 0 0
1 1 1 1 0

LOVELY PROFESSIONAL UNIVERSITY 75