Page 68 - DCAP108_DIGITAL_CIRCUITS_AND_LOGIC_DESIGNS

Unit 4: Minimization of Boolean Algebra

Comparing the previous SOP simplification, left, to the POS simplification, right, shows Notes
that the POS is the least cost solution. The SOP uses 5-gates total, the POS uses only 3-gates.
This POS solution even looks attractive when using TTL logic due to simplicity of the
result. We can find AND gates and an OR gate with 2-inputs.
Figure 4.15: SOP and POS Gate Diagrams

The SOP and POS gate diagrams are shown above for our comparison problem.

A tautology is a propositional formula that assigned truth value 1 by every
truth assignment of its propositional variables to an arbitrary Boolean algebra
(or, equivalently, every truth assignment to the two elements Boolean algebra).

Self Assessment

Choose the correct answer:
1. A maxterm is the product of N distinct literals where each literal occurs exactly once.
(a) True (b) False
2. The Sum- of-Products form represents an expression as a sum of minterms.
(a) True (b) False
3. ....................... expressions are easy to generate from truth tables.
(a) TTL (b) NAND

(c) SOP (d) POS
4. A ....................... is a logical product of many variables.
(a) Maxterm (b) Minterms
(c) Product term (d) Sum-terms
5. The examples of sum-of-products .......................

(a) (A + B ) (A + ) B (b) AB( + CB + ) ( C)
(c) (A + B )(A + ) B (d) AB + AB + AB
6. The examples of product-of-sums .......................

(a) AB + ABC + BC (b) A + AB + BC
(c) (A + B )(A + ) B (d) AB+ AB + AB
7. A product of sums expression consists of sum terms logically multiplied.
(a) True (b) False

LOVELY PROFESSIONAL UNIVERSITY 63