**Tom Kelliher, CS 240**

**Jan. 30, 2012**

*How to order the rows of a truth table*: 0 at the top; at
the bottom. Example: two-input AND.

Read 2.5.

Written assignment: Some of the Boolean manipulation problems are tricky -- start early.

Logic gates and Boolean algebra.

- Minterms and products
- Simplification using Karnaugh maps.

Karnaugh map manipulation; don't cares.

- What is a product? A sum?
- Definition of a minterm: A product term containing all literals,
complemented or not complemented.
Examples in three variables (, , ). Identify which are minterms and which are not: , , , .

- Sum of minterms. Can be derived directly from a truth table.
Example: sum output of a full binary adder. Derive truth table and sum of minterms equation. Observe and relationship to even parity (exclusive or).

- Product of sums form and difference from sum of minterms (products).

- A graphical tool for minimizing sum of minterm expressions.
- Two-variable maps:
- Structure; literal and value labels.
- Theory: Show simplification of
given
0 1 0 1 0 1 0 1 1 1 0 0

- Structure; literal and value labels.
- Three-Variable maps:
- Structure and connectivity.
- Examples: Sum and carry-out of full binary adder.

- Structure and connectivity.
- Four-Variable maps:
- Structure and connectivity.
- Example: Product bit 1 of two-bit multiplier. (Start with
``product'' table and then produce truth table for bit 1.)

- Structure and connectivity.
- Five-Variable maps? Higher?

Thomas P. Kelliher 2012-01-27 Tom Kelliher