Binary Adders

Within these castle walls be forged Mavens of Computer Science ...

— Merlin, The Coder

Half Adder

Prerequisites

• W1011 Number Systems
• W1012 Alternative Base Addition
• W1013 Boolean Algebra
• W1014 Logic Gates
• W1015 Bitwise Operations
• W1016 Logic Composition

Introduction

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. Let's consider what's required to add two, single-bit binary integers. We'll need one bit to represent the sum or the integers, and another to handle the carry. Representing this in the form of a truth table yields:

Inputs		Outputs
$A$	$B$	$C$	$S$
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.

Observe

Observe, Ponder, and Journal: Section 1

1. What truth table do you recognize that produces the output of the Carry column?
2. What truth table do you recognize that produces the output of the Sum column?