Combinational Logic Circuits
Tom Kelliher, CS26
Sept. 26, 1996
Applying logical operations to bytes, words, etc., on a bit-by-bit
- Register $8 contains 0x123.
- Register $9 contains 0xABC.
- Result of
and $10, $8, $9
- Result of
or $10, $8, $9
- How would you clear a bit or set of bits in a word?
- How would you set a bit or set of bits in a word?
- 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, and an implementation.
Why bother? Speed, power, real estate.
- Karnaugh Maps.
- Minimal cover.
- The map is a torus.
- 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?
Thomas P. Kelliher
Wed Sep 25 16:03:38 EDT 1996