Summary

1And in Conclusion$\dots$¶

Our goal this lecture was to build combinational logic blocks. We can summarize this approach with the following diagram:

We discussed how to convert among these three representations, as represented by the arcs in the diagram. Here is a summary:

• Truth-table to Boolean Expression. Write the canonical form (Sum-of-Products) and follow with algebraic simplification if desired.

• Boolean Expression to Truth-table. Evaluate expression for all input combinations and record output values.

• Boolean Expression to Gates. Use AND gates for the AND operators, OR gates for the OR operators, and inverters for the NOT operator. Wire up the gates the match the structure of the expression.

• Gates to Boolean Expression. Reverse the above process.

• Gates to Truth-table. Pass through all input combination and evaluate output.

• Truth-table to Gates. Map to Boolean expression then to gates.

2Textbook Readings¶

P&H A.3-A.6

3Additional References¶

These notes would not be possible without Professor John Wawrzynek’s CS 61C handouts:

• Boolean Handout