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.
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.
Find the decimal equivalent for binary 101010_{2}
= (0 x 2^{0}) + (1 x 2^{1}) + (0 x 2^{2}) + (1 x 2^{3}) + (0 x 2^{4}) + (1 x 2^{5})
= (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 101010_{2} is 42_{10}
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.
Find the hex equivalent for binary 110011011_{2}
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 110011011_{2} is 19B_{16}
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
Find the octal equivalent for binary 110011011_{2}
Split the given binary into group each containing 3 bits.
110 011 011
6 3 3
The equivalent octal value for the binary 110011011_{2} is 633_{8}
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
A | B | A + B | Carry |
---|---|---|---|
0 | 0 | 0 | 0 |
0 | 1 | 1 | 0 |
1 | 0 | 1 | 0 |
1 | 1 | 0 | 1 |
Add two binary numbers A = 10101_{2} & B = 10010_{2}
Solution :
10101
+10010
-------------
Sum 100111
-------------
Binary Subtraction
A | B | A - B | Borrow |
---|---|---|---|
0 | 0 | 0 | 0 |
0 | 1 | 1 | 1 |
1 | 0 | 1 | 0 |
1 | 1 | 0 | 0 |
Subtract binary A = 10101_{2} from B = 11010_{2}
Solution :
11010
-10101
-------------
Difference 101
-------------
Binary Multiplication
A | B | A x B |
---|---|---|
0 | 0 | 0 |
0 | 1 | 0 |
1 | 0 | 0 |
1 | 1 | 1 |
Multiply binary A = 10101_{2} with B = 101_{2}
Solution :
10101
x101
--------------
10101
00000
10101
----------------
Product 1101001
----------------
Binary Division
Find the Quotient & Remainder when dividing the binary number A = 111110_{2} by 1001_{2}
Solution :
110
--------------
1001)111110
1001
---------------
1101
1001
---------------
1000
---------------
Quotient = 110_{2} & Remainder = 1000_{2}
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.