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Number System: Binary, Decimal, Hexadecimal

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Converting Bits From Binary to Decimal

The following table shows how the bits in one octet are converted from binary code to a decimal value.

Binary code	Bit values	Decimal value
00000000	0	0
00000001	1	1
00000011	1+2	3
00000111	1+2+4	7
00001111	1+2+4+8	15
00011111	1+2+4+8+16	31
00111111	1+2+4+8+16+32	63
01111111	1+2+4+8+16+32+64	127
11111111	1+2+4+8+16+32+64+128	255

Convert the following binary numbers to decimal format.

Binary value	Decimal value
10001011	139
10101010	170
10111111 11100000 00000111 10000001	191.224.7.129
01111111 00000000 00000000 00000001	127.0.0.1

Convert the following decimal values to binary format.

Decimal value	Binary value
250	11111010
19	00010011
109.128.255.254	01101101 10000000 11111111 11111110
131.107.2.89	10000011 01101011 00000010 01011001

Use the calculator (scientific view) in the Accessories group to convert decimal format to binary format, and vice versa.

Hexadecimal

The other major numbering system used by computers is hexadecimal, or Base 16. In this system, the numbers are counted from 0 to 9, then letters A to F before adding another digit. The letter A through F represent decimal numbers 10 through 15, respectively. The below chart indicates the values of the hexadecimal position compared to 16 raised to a power and decimal values. It is much easier to work with large numbers using hexadecimal values than decimal.

To convert a value from hexadecimal to binary, you merely translate each hexadecimal digit into its 4-bit binary equivalent. Hexadecimal numbers have either and 0x prefix or an h suffix. For example, the hexadecimal number: 0x3F7A
Translates into, Using the Binary chart and the below chart for Hex:
0011 1111 0111 1010

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

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