**Tom Kelliher, CS 240**

**Feb. 1, 2012**

Read 2.6-2.8.

Written assignment due Friday.

Minterms and maps.

- Implicants and friends.
- Don't cares.

NAND gates, implementation, XOR, parity.

Consider . Diagram on K-map.

- A few implicants:
,
,
.
Not implicants: , .

- Prime Implicants:
,
, .
(Neither of the first two implicants are prime.)

- Essential prime implicants. All three of the prime implicants are
essential.
Example with non-essential prime implicant: . Prime implicants: , , . Essential prime implicants: , .

- Find prime implicants.
- Include all essential prime implicants.
- Include minimal number of remaining prime implicants to cover all
minterms.

Find all prime implicants, essential prime implicants, and simplify:

. (2-19(a))

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.

- Find all prime implicants, essential prime implicants, and simplify:
. (2-25(a))
- Real-world example. Consider a BCD to 7-segment display decoder.
Develop a simplified Boolean expression for the middle segment.

Thomas P. Kelliher 2012-01-31 Tom Kelliher