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)  

2^{7}  2^{6}  2^{5}  2^{4}  2^{3}  2^{2}  2^{1}  2^{0}  
128  64  32  16  8  4  2  1  
decimal number  0  
hexadecimal 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 2^{7} + 0 2^{6} + 1 2^{5} + 0 2^{4} + 0 2^{3} + 1 2^{2} + 0 2^{1} + 0 2^{0}
= 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  
hexadecimal 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
hexadecimal number  

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
= a_{16} 16^{1} + 4_{16} 16^{0 }
= 10 16^{1} + 4 16^{0 }
= 160 + 4
= 164
The hexadecimal number a4 from the calculator above can be converted to its decimal equivalent:
a4b3
= a_{16} 16^{3} + 4_{16} 16^{2}+ b_{16} 16^{1} + 3_{16} 16^{0 }
= 10 16^{3} + 4 16^{2} + 11 16^{1} + 3 16^{0 }
=40960 + 1024 + 176 + 3
= 42163
Hexadecimal vs. Decimal and Binary Numbers
For full table  rotate the screen!
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
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