Pertemuan:4 (Gate Minimization)

11/02/2013 07:35:00 AM (Basic) Digital Technique 0 Comments

In this section, the discusion is about :

The Map Method; Two-variable map and Three-variable map
Four-Variable Map
Five-variable Map
Product of Sums Simplification
Don’t-care Conditions
NAND and NOR Implementation
Other Two-Level Implementations
Exclusive-OR Function
Hardware Description Language (HDL)


The Map Method
Simplification of Boolean Expression
– Minimum # of terms, minimum # of literals
– To reduce complexity of digital logic gates
– The simplest expression is not unique

Methods:
– Algebraic minimization ⇒ lack of specific rules

Section 2.4
– Karnaugh map or K-map

Combination of 2, 4, … adjacent squares
Logic circuit ⇔ Boolean function ⇔ Truth table ⇔ K-map

Canonical form (sum of minterms, product of maxterms)
⇔ (Simplified) standard form (sum of products, product of sums)

Simplication Using Prime Implicant
Prime implicant: a product term obtained by combining the maximum possible number of adjacent squares in the map:
– A single 1 on a map represents a prime implicant if it is not adjacent to any other 1’s.
– Two adjacent 1’s form a prime implicant, provided that they are not within a group of four adjacent squares.
– Four adjacent 1’s form a prime implicant, provided that they are not within a group of eight adjacent squares.
– and so on
If a minterm in a square is covered by only one prime implicant, that prime implicant is said to be essential.

You can download full chapter from this link
BDT04-Gate Minimization