Computer Number Systems

Bits and Bytes

Computers store information in bits, which are labeled 0 (empty) or 1 (full).

A set of 8 bits is called a byte, like this: 1010 0010

Each byte has an address, which is labeled with a hexadecimal number, like this: C7.

Decimal, Hexadecimal, and Binary Numbers

Decimal Numbers

When we learn to count, we use Decimal numbers (0-10). The Decimal number system is also called Base 10, since after the number 9, we add a 0 for 10.

Hexadecimal Numbers

The address (location) of a byte is given in Hexadecimal numbers (0-F). This number system is called Base 16, since after the number 9, we use A, B, C, D, E, and F. After F, we add a 0 for 10.

Binary Numbers

Computers store information as Binary numbers (0-1). This number system is also called Base 2, since after the number 1, we add a 0 for 10.

Here is a chart to help you understand these numbers:

Decimal	Hexadecimal	Binary
0	0	0000 0000
1	1	0000 0001
2	2	0000 0010
3	3	0000 0011
4	4	0000 0100
5	5	0000 0101
6	6	0000 0110
7	7	0000 0111
8	8	0000 1000
9	9	0000 1001
10	A	0000 1010
11	B	0000 1011
12	C	0000 1100
13	D	0000 1101
14	E	0000 1110
15	F	0000 1111
16	10	0001 0000

Converting Binary Numbers to Decimal

Let’s convert the binary number 1001 1010 to a decimal number:

Binary=	1	0	0	1	1	0	1	0
	x128	x64	x32	x16	x8	x4	x2	x1
	=	=	=	=	=	=	=	=	Decimal
	128	+0	+0	+16	+8	+0	+2	+0	=154

This means that binary 1001 1010 = decimal 154.

Converting Hexadecimal to Decimal

Let’s convert the hexadecimal number C7F8 to a decimal number:

Hexadecimal=	C	7	F	8
	x4096	x256	x16	x1
	=	=	=	=	Decimal
	49152	+1792	+240	+8	=51192

This means that hexadecimal C7F8 = 51192 decimal.

Converting Hexadecimal to Binary

Hexadecimal numbers usually begin with 0x, which we don’t count when converting to binary. Let’s convert the hexadecimal number OxA2D3 to a binary number:

Hexadecimal=	A	2	D	3
	=	=	=	=
	1010	0010	1101	0011	=Binary

This means that hexadecimal 0xA2D3 = 1010 0010 1101 0011 binary.