Binary Calculator

Convert bits to decimal and back, or do integer add, subtract, multiply and divide on two binary strings — place values, not AND/OR/XOR.

How to use

Enter only 0 and 1 for binary fields, or a whole decimal to convert the other way.
Read the matching decimal or binary spelling.
For arithmetic, both sides are binary integers. Division must come out exactly.
Use hex when the worksheet is base 16, and the scientific calculator for decimal expressions.

How it works

Each binary digit is a power of two. 1010 = 8 + 0 + 2 + 0 = 10. 1111 = 15. 10000 = 16. Converting decimal to binary is repeated divide-by-2, remainders written last to first: 10 → 1010.

Adding 1010 + 110 is 10 + 6 = 16 = 10000. There is no carry UI; the result is the integer sum spelled in bits. Division of 101 by 10 is 5 ÷ 2, not an integer, so it is rejected.

Digits other than 0 and 1 are invalid. This is not bitwise AND, OR, XOR or a two’s-complement explainer. Safe-integer range keeps bits and decimal in lockstep.

Nibble grouping (4 bits) is how hex digits arise: 1111 = F. Use the hex page if that is the next step.

Leading zeros do not change the value: 01010 is still 10. People pad them to show a byte width (00001010). This page does not pad. A worksheet that switches from bits to hex mid-line should convert 1111 1010 as FA, not as a new arithmetic problem.

Formula

1010₂ = 8 + 2 = 10₁₀
1010₂ + 110₂ = 10000₂ (10 + 6 = 16)

Worked examples

Binary to decimal
1010 → 10
Add two binary numbers
1010 + 110 → 10000 (decimal 16)

Powers of two as bits

Binary	Decimal
1	1
10	2
100	4
1000	8
1010	10
1111	15
10000	16

Useful notes

Not a bitwise logic calculator.
Integer quotients only.
Only digits 0 and 1.

FAQ

How do I convert binary to decimal?: Add each digit times its place value: 1010 = 8 + 0 + 2 + 0 = 10.
How do I convert decimal to binary?: Repeatedly divide by 2 and read the remainders from last to first. 10 → 1010.
Why was my division rejected?: Only exact integer quotients are shown. 5 ÷ 2 is not a whole number, so 101 ÷ 10 has no binary integer result here.
What is 13 in binary?: 1101, because 8 + 4 + 0 + 1 = 13.
Does this do bitwise AND?: No. It converts and does integer + − × ÷. Bitwise operators are not on this page.

Related tools

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