Binary Calculator

Use our Binary Calculator for performing Addition, Subtraction, Multiplication and Division of Binary numbers. You can perform arithmetic operations (Add, Subtract, Multiply, or Divide) with Binary numbers using this Binary calculator. You can also use our Binary converter to convert base from Binary to Octal, Decimal, Hexadecimal etc.

Explore other calculators or unit converters or try out our Binary Calculator and learn more about Binary .

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Binary Calculator Details

What is Binary Number?

A binary number is a number expressed in the base-2 numeral system (binary numeral system). Binary numbers are represented by only two symbols or digits, i.e. 0 (zero) and 1(one)

Counting in Binary Number System

Decimal	0
Binary	0
Decimal	1
Binary	1
Decimal	2	3
Binary	10	11
Decimal	4	5	6	7
Binary	100	101	110	111
Decimal	8	9	10	11	12	13	14	15
Binary	1000	1001	1010	1011	1100	1101	1110	1111

Binary Arithmetic Operations – Add, Subtract, Multiply and Divide

Addition

0 + 0 = 0

0 + 1 = 1

1 + 0 = 1

1 + 1 = 0 carry 1 to the next column

When the result of an addition of digits exceeds the maximum permissible values then you have to carry the excess amount divided by the radix to the digit on left, so that it can be added to the next place value.

1 + 1 = 0 , 2/2 =1 and the remainder is 0; so 1 will be carried digit

Subtraction

0 – 0 = 0

0 – 1 = 1 borrow 1 to the next column

1 – 0 = 1

1 – 1 = 0

Conversion to and from other Numeral Systems

Binary to Decimal Conversion

Refer to our Number Base Converter to know about conversion from Decimal to Binary. Binary to Decimal conversion (from base 2 to Base 10) is simply inverse of the Decimal to Binary conversion process.

Multiply the digits (bits) of the binary number starting with the least significant (rightmost) bit with 2ⁿ and then add all of them. Here n is the position of the digit starting from the right assuming the position of the rightmost digit as 0.

Converting 11110 from Base 2 to Decimal

1 * 2⁴ + 1 * 2³ + 1 * 2² + 1 * 2¹+ 0 * 2⁰ = 30 in Decimal

Binary to Hexadecimal Conversion

Binary can be converted to hexadecimal by converting Binary to Decimal and then converting the Decimal number to Hexadecimal.

As Hexadecimal base 16 is power of 2, binary can also be converted directly to hexadecimal.

To convert a binary number to hexadecimal, divide the binary in groups of 4 bits starting from left.

111100₂ = 0011 1100 = 3C₁₆

Refer to our Hexadecimal Base Calculator and Conversion to know about conversion from Hexadecimal to Binary.

Binary to Octal Conversion

Binary can be converted to Octal by converting Binary to Decimal and then converting the Decimal number to Octal.

As Octal base 16 is power of 2, binary can also be converted directly to Octal.

To convert a binary number to Octal, divide the binary in groups of 3 bits starting from left.