How to use the Binary Calculator
- 1. Enter two binary numbersUse 0 and 1 only; a minus sign or 0b prefix is fine.
- 2. Pick the operationArithmetic, logic or shifts.
- 3. Read the resultBinary, decimal, hex and octal, with the column working for addition.
How binary arithmetic works
Binary uses only 0 and 1, and each column is worth double the one to its right: 1, 2, 4, 8, 16 and so on. The rules are short:
- Addition: 0+0 = 0, 0+1 = 1, 1+1 = 10 (write 0, carry 1), and 1+1+1 = 11 (write 1, carry 1).
- Subtraction: borrow from the next column, just like in decimal. Computers actually add the two's complement instead.
- Multiplication: shift and add. For each 1 in the multiplier, add a shifted copy of the other number.
- Division: long division, giving a whole-number quotient and a remainder.
Shifting left by one place doubles a number; shifting right halves it, dropping the remainder. Numbers of any length are handled exactly using JavaScript's BigInt, so even 200-bit values come out right.
Worked example
1011 + 0110: in decimal that's 11 + 6. Working from the right: 1+0 = 1; 1+1 = 0 carry 1; 0+1+1 = 0 carry 1; 1+0+1 = 0 carry 1; and the final carry gives a new leading 1. The answer is 10001, which is 17 in decimal, 11 in hex and 21 in octal. The tool lays out the carry row above the sum just as you'd write it on paper.
More to try:
1101 × 101= 1000001 (13 × 5 = 65).11001 ÷ 100= 110 remainder 1 (25 ÷ 4 = 6 remainder 1).1100 XOR 1010= 0110.
For fixed-width signed values with two's complement, such as what an 8-bit byte holds, use the Bitwise Operations Calculator.
Frequently asked questions
How are negative answers shown?
With a minus sign, like -101. For a negative result of subtraction, the tool also shows the 8-bit two's complement form.
Is there a size limit?
No practical one. BigInt keeps every digit exact.
Can I convert binary to decimal only?
Yes, the decimal value is shown for every result. The Number System Converter does plain conversions.
Is the binary calculator free to use?
Yes, the binary calculator is free and costs nothing. Your first calculation shows a short form for your name and WhatsApp number one time; once that's done, this tool and every other Uncodemy tool open with no form.