Number Systems

Binary

The Binary Number System is a cornerstone of digital technology. It is a base-2 numeral system that uses only two digits: 0 and 1. Each position in a binary number represents a power of 2, starting from the rightmost digit (which represents (2^0)).

Converting Decimal to Binary

Convert the decimal number 5 to its binary representation.

Divide the number by 2 and note the remainder.

5 ÷ 2 = 2 remainder 1

Continue dividing the quotient by 2 until the quotient is zero.

2 ÷ 2 = 1 remainder 0
1 ÷ 2 = 0 remainder 1

Read the remainders from bottom to top:

Binary representation of 5 is 101.

Converting Decimal to Binary

Convert the binary number 101 back to its decimal representation.

Write down the binary number and assign each digit a power of 2, starting from the rightmost digit (which represents (2^0)).

101₂ = 1 * (2^2) + 0 * (2^1) + 1 * (2^0)

Calculate each term and sum them up.

1 * (2^2) = 4
0 * (2^1) = 0
1 * (2^0) = 1

4 + 0 + 1 = 5

So, the binary number 101 represents the decimal number 5.

Octal

Hexidecimal

Decimal

ASCII

Table of Conversions

Binary	Octal	Hexadecimal	Decimal	ASCII
000000	0	0	0	NUL
000001	1	1	1	SOH
000010	2	2	2
000011	3	3	3
000100	4	4	4
000101	5	5	5
000110	6	6	6	ACK
000111	7	7	7
001000	10	8	8
001001	11	9	9
001010	12	A	10	LF
001011	13	B	11
001100	14	C	12
001101	15	D	13	CR
001110	16	E	14
001111	17	F	15	NAK
101001	71	41	65	A
101010	72	42	66	B
101011	73	43	67	C
101100	74	44	68	D
101101	75	45	69	E
101110	76	46	70	F
101111	77	47	71	G
110000	80	48	72	H
110001	81	49	73	I
110010	82	4A	74	J