Difference between revisions of "Binary Adders"
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This is formally termed a '''full-adder''', a logic circuit capable of adding three bits. | This is formally termed a '''full-adder''', a logic circuit capable of adding three bits. | ||
== Key Concepts == | == Key Concepts == | ||
== Exercises == | == Exercises == |
Revision as of 15:34, 29 July 2019
Prerequisites[edit]
- W1011 Number Systems
- W1012 Alternative Base Addition
- W1013 Boolean Algebra
- W1014 Logic Gates
- W1015 Bitwise Operations
- W1016 Logic Composition
Introduction[edit]
One of the most fundamental operations performed by computers, aside from the logical operations that we've already discussed, is the arithmetic operation of addition.
Half-Adder[edit]
Let's consider what's required to add two, single-bit binary integers. We'll need one bit to represent the sum of the integers, and another to handle the carry. Representing this in the form of a truth table yields:
Inputs | Outputs | ||
---|---|---|---|
0 | 0 | 0 | 0 |
0 | 1 | 0 | 1 |
1 | 0 | 0 | 1 |
1 | 1 | 1 | 0 |
This is formally termed a half-adder, a logic circuit capable of adding two bits.
- What truth table do you recognize that produces the output of the Carry column?
- What truth table do you recognize that produces the output of the Sum column?
Full-Adder[edit]
In order to add two single-bit binary integers PLUS a carry, we need an adder capable of adding three single-bit binary numbers. Again, we'll need one bit to represent the sum of the integers, and another to handle the carry. Representing this in the form of a truth table yields:
Inputs | Outputs | |||
---|---|---|---|---|
0 | 0 | 0 | 0 | 0 |
0 | 0 | 1 | 0 | 1 |
0 | 1 | 0 | 0 | 1 |
0 | 1 | 1 | 1 | 0 |
1 | 0 | 0 | 0 | 1 |
1 | 0 | 1 | 1 | 0 |
1 | 1 | 0 | 1 | 0 |
1 | 1 | 1 | 1 | 1 |
This is formally termed a full-adder, a logic circuit capable of adding three bits.