Binary Calculator · Practical guide
How to Multiply Binary Numbers
Binary multiplication is just shifting and adding — there are no times tables to memorize.
At a glance
Shift and Add
Binary multiplication needs no times tables, because each digit is 0 or 1. For every 1 in the second number, copy the first number shifted left by that digit's position, then add the copies together. Multiplying by 0 contributes nothing.
Interactive tool
Binary Calculator
Enter your own values, then compare the result with the examples below.
Result
Worked Example: 101 × 11
- Multiply 101 by the rightmost 1:
101 - Multiply 101 by the next 1, shifted one place left:
1010 - Add the partial products:
101 + 1010 = 1111
So 101 × 11 = 1111.
Check in Decimal
101 is 5 and 11 is 3, and 5 × 3 = 15. Binary 1111 = 8 + 4 + 2 + 1 = 15, and the hexadecimal form is 0xF. The calculator above confirms all three formats in one pass, including the decimal step line.
Why Computers Love This
Shifting left by one place doubles a binary number, just as appending a zero multiplies a decimal number by ten. Processors multiply using exactly this shift-and-add pattern in hardware, so understanding it explains both the math and the machine.
Division Is the Reverse
Binary division mirrors long division: for example, 1100 ÷ 0011 = 100 (12 ÷ 3 = 4). If the division is uneven, the tool shows the decimal quotient, such as 111 ÷ 010 = 3.5.
Frequently Asked Questions
What is the binary multiplication table?
It has only three facts: 0 × 0 = 0, 0 × 1 = 0, and 1 × 1 = 1. Anything times 0 is 0, and anything times 1 is itself.
How do I multiply a binary number by 2 quickly?
Append a 0 on the right (shift left one place). 101 shifted once is 1010, doubling 5 to 10.
Can binary multiplication produce fractions?
Multiplying whole binary numbers always gives a whole number. Fractional binary values exist but this calculator works with integers.
How do I check a binary multiplication by hand?
Convert both factors to decimal, multiply, then convert back. 110 × 101 = 6 × 5 = 30 = 11110 in binary.