Binary Converter | Convertopedia

Use the below binary converter to convert Binary values to Decimal, Hexadecimal and Octal values.

Binary Number		₂

Decimal Number		₁₀
Octal Number		₈
Hexadecimal Number		₁₆

Enter any binary number to this binary converter and click on convert button to convert binary to decimal, hexadecimal and octal.

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Binary Number

Binary numbering system uses only two symbols 0 and 1. Each digits of a binary number is referred to as bits. Binary system is also known as base -2 system. Each digit is represented by the increasing power of 2 from the LSB (Least Significant Bit). Binary system is the heart of digital electronics and is used for information flow. In digital electronics, 0 and 1 are used to denote logic states, high and low. Arithmetic operations are also possible in binary system.

Decimal Number

Whole number, a decimal point and a fractional value combines to form a decimal number. The decimal point separates the whole number part from the fractional part of the number. Each digit of a decimal number can be any number from 0 to 9. Any value less than 1 is written to the right of decimal point. Decimal numbers are also known as base-10 number or counting numbers. Place value of decimal number varies as the whole number powers of 10 starting from the left of decimal point. Similarly, the place value of digits left to decimal point varies as the division of power of tens.

Hexadecimal Number

Hexadecimal number system uses 16 different symbols to represent a numeric value. It uses numbers 0 to 9 and alphabets A to F for representation. . The place value of each digits of an hexadecimal number varies as the whole number powers of 16 starting from the right (Least Significant Digit). The first single digit number in hexadecimal system is 0 and the last is F. Similarly, the first two digit hexadecimal number is 10 and the last is FF and so on. It is used as an alternative for binary numbers by developers and programmers.

Octal Number

Octal numbers use digits from 0-7 only. It is known as base-8 number. The place value of each digits of an octal number varies as the whole number powers of 8 starting from the right (Least Significant Digit). The first single digit number in octal system is 0 and the last is 7. Similarly, the first two digit octal number is 10 and the last is 77 and so on. Octal number system was widely used in early computers.

Binary to decimal Conversion

Example: Convert 1111₂ to decimal number

A binary number can be converted into decimal number using the following formula:

Decimal Number = (D_n X 2ⁿ+ …………… + D₂ X 2²+ D₁ X 2¹+ D₀ X 2⁰).

Where,

D_n– D₀→ digits of a binary number.

Decimal number = (1 X 2³ + 1 X 2² + 1 X 2¹+ 1 X 2⁰) = 8 + 4 + 2 + 1 = 15₁₀

Binary to Octal Conversion

Example: Convert 1111₂ to octal number

Split binary number into sets of three digits starting from the LSB. Note down the decimal number corresponding to each sets of three digits to convert binary number to octal number.

In this example 1111, 1111 can be rewritten as 001-111. Writing down the decimal number corresponding to the digits: 001→1 ,111→1.

So 1111₂ = 17₈

Binary to Hexadecimal Conversion

Example: Convert 1111₂ to hexadecimal number

Split binary number into sets of four digits starting from the LSB. Note down the hexadecimal number corresponding to each sets of four digits to convert binary number to hexadecimal number. (Refer the below table).

In this example 1111, 1111 can be rewritten as 0000-1111. Writing down the decimal number corresponding to the digits: 0000→0 ,1111→F.

So 1111₂ = F₁₆

Binary, Decimal, Octal and Hexadecimal conversion table

Binary	Decimal	Octal	Hexadecimal
0001	01	01	01
0010	02	02	02
0011	03	03	03
0100	04	04	04
0101	05	05	05
0110	06	06	06
0111	07	07	07
1000	08	10	08
1001	09	11	09
1010	10	12	0A
1011	11	13	0B
1100	12	14	0C
1101	13	15	0D
1110	14	16	0E
1111	15	17	0F