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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.

About Michael Boguslavskiy

Michael Boguslavskiy is a full-stack developer & online presence consultant based out of New York City. He's been offering freelance marketing & development services for over a decade. He currently manages Rapid Purple - and online webmaster resources center; and Media Explode - a full service marketing agency.

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