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.


== Topic Headers ==
== Key Concepts ==
== Key Concepts ==
== Exercises ==
== Exercises ==

Revision as of 15:34, 29 July 2019

Within these castle walls be forged Mavens of Computer Science ...
— Merlin, The Coder
Half Adder

Prerequisites[edit]

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.

ObserveObserveIcon.png
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?


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.

Key Concepts[edit]

Exercises[edit]

Template:W1017-Exercises

References[edit]