Combinational Logic Circuits
Tom Kelliher, CS26
Oct. 1, 1996
- Given a logic expression, how do we implement it?
- Every Boolean expression can be represented in sum of
- Implementing SOP expressions.
Convert each of the following to SOP notation and draw a logic circuit,
using AND, OR, and inverter gates, implementing it:
- XY + YZ.
- Implement a binary full adder. Here is the truth table:
Start by writing the SOP equation.
BTW, is this a useful function?
- Consider a five-input Boolean function that is asserted whenever
exactly two of its inputs are asserted. Construct its truth table, its
SOP equation(s), and an implementation.
Why bother? Speed, power, real estate.
- Karnaugh Maps.
- Minimal cover.
- The map is a sphere.
- Don't cares in real circuits.
- Gray code numbering.
- Converting the covers to equations.
Try the following:
- The sum output of a full binary adder.
- The carry out output of a full binary adder.
- A circuit which compares two-bit unsigned numbers. There are three
outputs: inputs equal, first greater, second greater.
Why do TTL and CMOS designers use these gates?
Why are ECL designers so lucky?
- Design and implement a 2-1 multiplexer, using a K-map for
minimization of the output equation. Here's the truth table:
A multiplexer works like a switch. One way of drawing them is:
- Design and implement a circuit to take a BCD-encoded digit and drive
a seven-segment display (used in watches and calculators). Use a K-map to
minimize each of the seven output equations. Here is the labeling for the
Thomas P. Kelliher
Mon Sep 30 09:23:07 EDT 1996