Question 1

How do I add two binary numbers?

Accepted Answer

Align the two numbers bit by bit from the right. Add each column, then add any carry from the previous column (just like decimal addition). The carry rule is: 0+0=0, 0+1=1, 1+1=10 (write 0 carry 1), 1+1+1=11 (write 1 carry 1). Example: 1011 (11) + 1101 (13) = 11000 (24).

Question 2

How does binary subtraction work?

Accepted Answer

You can subtract directly or use the two's complement trick: 1) Find the two's complement of the subtrahend (invert bits and add 1). 2) Add it to the minuend. 3) Discard the carry. Negative results are returned in two's complement form.

Question 3

What is two's complement?

Accepted Answer

Two's complement is the most common way to represent signed integers in binary. To get the two's complement of a number, invert all its bits and add 1. For example, the 8-bit two's complement of 5 (00000101) is 251 (11111011), which represents -5. The highest bit is the sign bit.

Question 4

Can I do bitwise operations in this calculator?

Accepted Answer

Yes. Switch to Bitwise mode to compute AND, OR, XOR, NOT, left shift (<<) and right shift (>>) between two binary numbers. The calculator automatically limits the result to a fixed bit width and shows it in binary, decimal, hex and octal.

Question 5

What is the largest binary number this calculator handles?

Accepted Answer

The calculator handles up to 64 bits, which is more than enough for any unsigned integer JavaScript can represent natively (2^53 - 1). For values larger than that it operates as if it were a BigInt-like string, which is exact for addition/subtraction and approximate for multiplication/division.