Binary Calculator

What the binary calculator does

This is the all-in-one binary calculator. It adds, subtracts, multiplies, and divides binary numbers, whichever you choose, and shows the result in both binary and decimal. Enter two numbers, pick an operation, and read off the answer.

If you find yourself doing several different binary sums, this saves hopping between separate tools. One set of inputs, a dropdown for the operation, and you are set.

How to use it

1. Choose a bit size. This sets how wide your numbers are, with 8 as the default.
2. Enter the two binary numbers. Type each one using only 0s and 1s.
3. Pick an operator. Choose addition, subtraction, multiplication, or division from the dropdown.
4. Press Calculate. The result appears as both a binary result and a decimal result.

Press Reset to clear the inputs.

The four operations at a glance

Each operation runs on the same column methods as ordinary arithmetic, with binary's two digits changing the details. Here is the shape of each, in brief:

• Addition works column by column with carries, and the thing to remember is that 1 + 1 is 10, so you write 0 and carry 1.
• Subtraction works column by column with borrows, where a borrow is worth 2, so a borrowed 0 becomes 2 and 2 - 1 = 1.
• Multiplication is shift and add: each row is either zeros or a copy of the top number, shifted to its place, with no times tables at all.
• Division is long division where the divisor fits either zero or one times, and the result can carry on past a binary point into a fraction.

Each of these also has its own focused calculator if you want to walk through one in more depth.

A worked example with real numbers

Say you pick addition and enter 110 and 101. Working right to left: 0 + 1 = 1, then 1 + 0 = 1, then 1 + 1 = 10, so write 0 and carry 1, and that carry becomes a new leading 1. The result reads 1011. To check it, 110 is 6 and 101 is 5, and 6 + 5 is 11, which is what 1011 comes to.

Leave the numbers as they are and switch the operator, and the calculator applies that operation's method instead. The same 110 and 101 under multiplication, for instance, follow the shift-and-add steps rather than the carry steps.

Reading the result

Every calculation shows you two things: the answer in binary and the same answer in decimal, so you can read whichever you need and use the decimal as a quick check. A couple of results look a little different from the rest. Division can produce a binary point when the numbers do not divide evenly, giving something like 101.1 rather than a whole number. And for large products or sums, give yourself a bit size with enough room, since results can be wider than the numbers you put in.

Questions people ask

Which operations does it handle?

All four: addition, subtraction, multiplication, and division. You pick the one you want from the operator dropdown before calculating.

How do I switch operations?

Choose a different option in the operator dropdown and press Calculate again. The two numbers stay as they are, so you can try several operations on the same pair.

Does it show the decimal answer too?

Yes. Every result appears in both binary and decimal, which makes it easy to check the binary against a value you recognize.

Does it work the way I would by hand?

The answer is the same as the hand methods give: carries for addition, borrows for subtraction, shift and add for multiplication, and long division for division. The decimal result confirms each one.

References

1. Weisstein, Eric W. "Binary." From MathWorld, A Wolfram Resource. https://mathworld.wolfram.com/Binary.html