# Implicant Simplification and Don't Cares

Tom Kelliher, CS 240

Feb. 5, 2010

### Assignment

Written assignment due Monday.

### From Last Time

Minterms and maps.

### Outline

1. Implicants and friends.

2. Don't cares.

### Coming Up

NAND gates, implementation, XOR, parity.

# Implicants and Friends

Consider . Diagram on K-map.

1. A few implicants: , , .

Not implicants: , .

2. Prime Implicants: , , .

(Neither of the first two implicants are prime.)

3. Essential prime implicants. All three of the prime implicants are essential.

Example with non-essential prime implicant: . Prime implicants: , , . Essential prime implicants: , .

## Simplifying an Expression

1. Find prime implicants.

2. Include all essential prime implicants.

3. Include minimal number of remaining prime implicants to cover all minterms.

## Example

Find all prime implicants, essential prime implicants, and simplify:
. (2-19(a))

# Don't Cares

Simply: for invalid input values, we don't care what the output value is.

Also: we simply don't care what the output value is for a particular input value.

## Examples

1. Find all prime implicants, essential prime implicants, and simplify: . (2-25(a))

2. Real-world example. Consider a BCD to 7-segment display decoder. Develop a simplified Boolean expression for the middle segment.

Thomas P. Kelliher 2010-02-04
Tom Kelliher