Binary Calculator

Binary calculator - An all-in-one and easy to use online tool for binary to decimal, binary to hex and binary to octal conversion, and generate work with steps. It also supports binary addition, subtraction, multiplication and division operations with more precise results.

Examples

Binary to Decimal Conversion

The binary to decimal conversion can be made through summation of multiplication of each bit with increasing power of 2 from the right to left of the binary number. Refer this below workout to understand how to convert base-2 binary to base-10 decimal number, or use this binary calculator to easily find out the decimal equivalent for a given binary number.

Example :
Find the decimal equivalent for binary 101010₂
         = (0 x 2⁰) + (1 x 2¹) + (0 x 2²) + (1 x 2³) + (0 x 2⁴) + (1 x 2⁵)
         = (0 x 1) + (1 x 2) + (0 x 4) + (1 x 8) + (0 x 16) + (1 x 32)
         = 0 + 2 + 0 + 8 + 0 + 32
         = 42
The decimal equivalent for binary 101010₂ is 42₁₀

Use this binary to decimal converter calculator for quick conversions, arithmetic operations and to generate the complete step by step work for such conversions.

Binary to Hex Conversion

The binary to hex conversion can be made by grouping of digits. Make the given binary number into groups, each containing 4 bits from right to left. If the last group is short of 4 bits, add zeros to the left to make it 4 bits. Find the hex equivalent for each group and write it down in the same order and provide the equivalent hex number for the given binary number. Refer this below workout to understand how to convert base-2 binary to base-16 hex number, or use this binary calculator to easily find out the hex equivalent for a given binary number.

Example :
Find the hex equivalent for binary 110011011₂
Split the given binary into group each containing 4 bits.
        1     1001     1011
The third group short of 3 bits, so add 0’s to the left to make it 4 bits
      0001     1001     1011

      1             9           B
The equivalent hex value for the binary 110011011₂ is 19B₁₆

Use this binary to hex converter calculator for quick conversions, arithmetic operations and to generate the complete step by step work for such conversions.

Binary to Octal Conversion

The binary to octal conversion can be made by grouping of digits. Make the given binary number into groups, each containing 3 bits from right to left. If the last group is short of 3 bits, add zeros to the left to make it 3 bits. Find the octal equivalent for each group and write it down in the same order and provide the equivalent hex number for the given binary number. Refer this below workout to understand how to convert base-2 binary to base-8 octal number, or use this binary calculator to easily find out the octal equivalent for a given binary number.

EXample :
Find the octal equivalent for binary 110011011₂
Split the given binary into group each containing 3 bits.
110 011 011

6 3 3
The equivalent octal value for the binary 110011011₂ is 633₈

Use this binary to octal converter calculator for quick conversions and to generate the complete step by step work for such conversions.

Binary Numbers Arithmetic
Learn how to perform addition, subtraction, multiplication & division between two or more binary numbers from the below information.

Binary Addition

Refer the below binary addition truth table and example to understand how to carry out binary addition, or use this binary calculator to easily find out the sum of two or more binary numbers.

A	B	A + B	Carry
0	0	0	0
0	1	1	0
1	0	1	0
1	1	0	1

EXample :
Add two binary numbers A = 10101₂ & B = 10010₂

Solution :
              10101
            +10010
            -------------
  Sum   100111
            -------------

Binary Subtraction

Refer the below binary subtraction truth table and example to understand how to carry out binary subtraction, or use this binary calculator to easily find out the difference between two or more binary numbers.

A	B	A - B	Borrow
0	0	0	0
0	1	1	1
1	0	1	0
1	1	0	0

EXample :
Subtract binary A = 10101₂ from B = 11010₂

Solution :
                    11010
                   -10101
                  -------------
Difference       101
                  -------------

Binary Multiplication

Refer the below binary multiplication truth table and example to understand how to carry out binary multiplication, or use this binary calculator to easily find out the product of two or more binary numbers.

A	B	A x B
0	0	0
0	1	0
1	0	0
1	1	1

Example :
Multiply binary A = 10101₂ with B = 101₂

Solution :
                    10101
                      x101
                --------------
                    10101
                  00000
                10101
                ----------------
Product   1101001
                ----------------

Binary Division

Refer the below binary division truth table and example to understand how to carry out binary division, or use this binary calculator to easily find out the quotient and remainder of a binary number divided by another.

Example :
Find the Quotient & Remainder when dividing the binary number A = 111110₂ by 1001₂

Solution :
                  110
                --------------
       1001)111110
                1001
                ---------------
                     1101
                     1001
                ---------------
                     1000
                ---------------

Quotient = 110₂ & Remainder = 1000₂

Use this binary converter calculator for quick arithmetic operations between addition, subtraction, multiplication & division between two or more binary numbers or within this number system.