Enter two binary numbers and choose an operation — addition, subtraction, multiplication, or division — to get the binary result along with its decimal and hexadecimal equivalents. You can also convert a binary number to decimal or a decimal number to binary using the conversion fields below.
Binary Result
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Decimal Result
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Hexadecimal Result
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Binary → Decimal
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Decimal → Binary
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A binary number is expressed in base-2, using only the digits 0 and 1. Each digit is called a bit. For example, the decimal number 10 is represented as 1010 in binary, and 100 in decimal is 1100100 in binary.
Binary addition follows the same column-by-column rules as decimal addition, but with only two digits. Key rules: 0+0=0, 0+1=1, 1+1=10 (write 0, carry 1), and 1+1+1=11 (write 1, carry 1). For example, 1101 + 1010 = 10111.
Binary subtraction is similar to decimal subtraction. When the top digit is smaller than the bottom digit, you borrow from the next higher bit. For example, 1101 − 1010 = 0011. Negative results occur when the second number is larger than the first.
Multiply each binary digit by 2 raised to the power of its position (starting from 0 on the right), then sum the results. For example, 1101 in binary = (1×8) + (1×4) + (0×2) + (1×1) = 13 in decimal.
Repeatedly divide the decimal number by 2 and record the remainders. Reading the remainders from bottom to top gives the binary representation. For example, 25 ÷ 2 gives remainders 1,0,0,1,1, so 25 in decimal = 11001 in binary.
Hexadecimal (base-16) uses digits 0–9 and letters A–F. It is closely related to binary because each hex digit corresponds exactly to a 4-bit binary group. For example, binary 1111 = hex F, and binary 1010 = hex A, making conversions straightforward.
Yes. In computing, negative binary numbers are typically represented using two's complement notation. This calculator shows the arithmetic result; if your subtraction yields a negative number, the decimal result will be negative.
Binary division works like long division in decimal, but only using 0s and 1s. The calculator computes the quotient as a decimal value when binary division results in a non-terminating binary fraction. For example, 1100 ÷ 0011 = 100 (i.e., 12 ÷ 3 = 4).