Introduction

Data representation refers to the way that values are stored in a computer. For technical reasons, computers do not use the familiar base-10 number system but rather avail themselves of the base-2 (binary) system. Under this paradigm, numbers are represented as 1's and 0's.

Integer Representation

When storing an integer value, there are two ways to represent it - signed and unsigned - depending on whether the value should be entirely non-negative or may also have a "-" sign. Based on the number of bits used for storing a value, the value may have a different range.

Size	Range Size	Unsigned Range	Signed Range
Byte (8 bits)	$2^{8}$	$[0..255]$	$[- 128.. + 127]$
Word (16 bits)	$2^{16}$	$[0..65, 535]$	$[- 32, 768.. + 32, 767]$
Doubleword (32 bits)	$2^{32}$	$[0..4, 294, 967, 295]$	$[- 2, 147, 483, 648.. + 2, 147, 483, 647]$
Quadword (64 bits)	$2^{64}$	$[0.. 2^{64} - 1]$	$[- 2^{63} .. + 2^{63} - 1]$
Double Quadword (128 bits)	$2^{128}$	$[0.. 2^{128} - 1]$	$[- 2^{127} .. + 2^{127} - 1]$

Unsigned integers are represented in their typical binary form.

Two's Complement

Signed integers are represented using two's complement. In order to convert a acquire the negative form of a number in two's complement, is two negate all of its bits and add 1 to the number. A corollary of this representation is that it adds no complexity to the addition and subtraction operations.

The Cyberclopaedia

Introduction

Integer Representation

Two's Complement