Table of Contents
Lab Work 2 (Part 2)
Adders and Comparators
One of the most useful combinational logic circuit is an adder. It is the core component of any Arithmetic Unit - used in binary multipliers and even floating-point arithmetic units. Meanwhile, a comparator is useful as a decision making circuitry - it usually compares the magnitude of two binary values.
Half-Adder
A half-adder sums two 1-bit values and provides two 1-bit values (sum and carry).
| Half-Adder | |
|---|---|
| Symbol | Truth Table |
 |  |
Disclaimer: The images above are extracted from resources available for Digital Fundamentals 11th Edition (Global Edition)
Full-Adder
A full-adder sums three 1-bit values and provides two 1-bit values (sum and carry).
| Full-Adder | |
|---|---|
| Symbol | Truth Table |
 |  |
Disclaimer: The images above are extracted from resources available for Digital Fundamentals 11th Edition (Global Edition)
Comparator
There are three possible output bits of a comparator (depending on application requirement): equality (==), less than (<) and greater than (>).
| Comparator Output | Description |
|---|---|
EQ (==) | Output is at logic HI when the first value is exactly the same as the second value |
LT (<) | Output is at logic HI when the first value is less than the second value |
GT (>) | Output is at logic HI when the first value is greater then the second value |
Truth Table for a 1-bit Comparator:
| A | B | EQ | LT | GT |
|---|---|---|---|---|
| 0 | 0 | 1 | 0 | 0 |
| 0 | 1 | 0 | 1 | 0 |
| 1 | 0 | 0 | 0 | 1 |
| 1 | 1 | 1 | 0 | 0 |
Note: A 2-bit comparator cannot be built by simply cascading two 1-bit logic circuits.
Things To Do
THING 1 Build a 1-bit half-adder circuit and verify.
THING 2 Build a 1-bit full-adder circuit using 2×1-bit half-adders. Verify. Trivia: What is the least number of ICs (of 2-input logic gates) needed to implement this?
THING 3 (Optional?) Build a 2-bit adder and verify.
THING 4 (Optional?) Construct a truth table for 1-bit subtractor. Build the circuit and verify.
THING 5 (Optional?) Build a 4-bit ripple carry adder and verify.
THING 6 (Optional?) Build a 4-bit carry look ahead (CLA) adder and verify.
THING 7 Construct a truth table for 2-bit comparator (3 outputs). Get the Boolean expression for each output. Build the circuit and verify.
THING 8 (Optional?) Build a 4-bit comparator (3 outputs) and verify.
ask your instructor for more…