Binary Converter & Calculator

Binary converter calculator to perform binary to decimal, binary to hex & binary to octal conversion, steps for work & all arithmetic operations between decimal, binary, hex & octal number system.

Binary Number
Binary number is the base-2 number system only uses 0 and 1 to represent any values, is the most commonly used system in digital electronics & communication.

Example Conversion with Work

How to convert binary to decimal?

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.

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.

How to convert binary to hex?

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 provides the equivalent hex number for the 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.

How to convert binary to octal?

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 provides the equivalent hex number for the 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.

How to perform binary addition?

The binary addition can be performed by using the below binary addition truth table.

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
            -------------

How to perform binary subtraction?

The binary subtraction can be performed by using the following binary subtraction truth table.

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
                  -------------

How to perform binary multiplication?

The binary multiplication can be performed by using the following binary multiplication truth table.

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
                ----------------

How to perform binary division?

The binary division can be performed by successive subtraction method.

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.