# Binary to Decimal, Hexadecimal and ASCII Converter

## Convert between binary, decimal and hexadecimal numbers

### Binary - to Decimal, Hexadecimal and ASCII Converter

Click on the binary number buttons to toggle between 0 and 1 for each bit:

unsigned
binary number
(8 bits, one byte)
27 26 25 24 23 22 21 20
128 64 32 16 8 4 2 1
decimal number 0
ASCII

A binary number is a number expressed in the binary numeral system or base 2 numeral system. A binary number can express any number by using only two digits: 0 and 1. The calculator above converts binary numbers with 1 to 8 bits (one byte) to the decimal or hexadecimal equivalents.

The default 8 bit (one byte) binary number 10100100 is calculated to the decimal equivalent:

10100100

= 1 27 + 0 26 + 1 25 + 0 24 + 0 23 + 1 22 + 0 21 + 0 20

= 128 + 0 + 32 + 0 + 0 + 4 + 0 + 0

= 164

8 bits or byte can be used to represent an ASCII (American Standard Code for Information Interchange) alphabetic character - like the binary number 01000001, or decimal number 65, representing A.

### Decimal - to Binary, Hexadecimal and ASCII Converter

decimal number
binary number
ASCII

The standard numeral system is called decimal with base 10 and uses 10 symbols: 0,1,2,3,4,5,6,7,8,9.

### Hexadecimal - to Binary, Decimal and ASCII Converter

binary number
decimal number
ASCII

The hexadecimal (also base 16, or hex) is a positional numeral system with base 16.

The hexadecimal system use sixteen distinct symbols with 0–9 representing the values zero to nine and A, B, C, D, E, F (or a, b, c, d, e, f) representing the values ten to fifteen.

The default hexadecimal number  a4 from the calculator above can be converted to its decimal equivalent:

a4

= a16 161 + 416 160

= 10 161 + 4 16

= 160 + 4

= 164

The hexadecimal number a4 from the calculator above can be converted to its decimal equivalent:

a4b3

= a16 163 + 416 162 + b16 161 + 316 160

= 10 163 + 4 162 + 11 161 + 3 16

=40960 + 1024 + 176 + 3

= 42163

#### Hexadecimal vs. Decimal and Binary Numbers

 Hexadecimal Number 0 1 2 3 4 5 6 7 8 9 a b c d e f Decimal Number 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Binary Number 0000 0001 0010 0011 0100 0101 0110 0111 1000 1001 1010 1011 1100 1101 1110 1111

Each hexadecimal digit represents four binary bits - a nibble. Four digital bits can represent up to 16 different values. Two nibbles with 8 bits is a byte. Computers use mostly bytes or multiplies of bytes (16, 32, 64 .. bits) in their operations.

Binary representation of the hexadecimal number

a4

= 1010 0100

Binary representation of the hexadecimal number

a4b3

= 1010 0100 1011 0011

## Related Topics

• Mathematics - Mathematical rules and laws - numbers, areas, volumes, exponents, trigonometric functions and more

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