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Browse all calculatorsAdd, subtract, multiply and divide binary numbers and see every step. Bitwise operations and two’s complement included.
Looking to convert text? This page does math on binary numbers. To turn letters into 0s and 1s, use the text to binary translator, or decode binary back into words with the binary to text converter.
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A binary calculator does arithmetic on base-2 numbers, which use only the digits 0 and 1. It adds, subtracts, multiplies and divides binary values, and many also convert to decimal and run bitwise operations. This one works with binary numbers of any length and shows the carries, borrows and remainders behind each answer.
Binary is a place-value system like decimal, except each place is worth twice the place to its right, so 1011 means 8 + 0 + 2 + 1 = 11. The rules are the same as in school arithmetic with two digits: 1 + 1 = 10, which writes 0 and carries 1. This calculator is about numbers. If you want to turn words into binary, use the binary translator, or paste binary into the binary to text converter to read the message.
| Binary | Decimal check |
|---|---|
| 1 + 1 = 10 | 1 + 1 = 2 |
| 1011 + 110 = 10001 | 11 + 6 = 17 |
| 1010 – 11 = 111 | 10 – 3 = 7 |
| 101 × 11 = 1111 | 5 × 3 = 15 |
| 1101 ÷ 10 = 110 remainder 1 | 13 ÷ 2 = 6 remainder 1 |
| 10101010 + 11001100 = 101110110 | 170 + 204 = 374 |
| 11001100 AND 10101010 = 10001000 | 204 AND 170 = 136 |
Four steps, and the answer updates as you type.
Arithmetic adds, subtracts, multiplies and divides. Bitwise runs AND, OR, XOR, NOT and shifts. Convert changes binary to decimal or decimal to binary.
Use only 0 and 1. Leading zeros, spaces, underscores and a 0b prefix are fine. Tap the plus-minus button or type a minus sign for a negative number. Any other digit is named in a message.
The answer appears in binary, decimal, hexadecimal and octal. Pick 8, 16, 32 or 64 bits to see the two’s complement pattern and whether the result overflows.
Open Show the working to see the carries, borrows, partial products, long-division table or place values. Copy the result, send it on as the next A, or share a link.
The single-bit rules behind every answer, plus the tables people look up most.
| A and B | A + B | A – B | A × B |
|---|---|---|---|
| 0 and 0 | 0 | 0 | 0 |
| 0 and 1 | 1 | 1 (borrow 1 from the left) | 0 |
| 1 and 0 | 1 | 1 | 0 |
| 1 and 1 | 10 (write 0, carry 1) | 0 | 1 |
| Power | Decimal | Binary |
|---|---|---|
| 20 | 1 | 1 |
| 21 | 2 | 10 |
| 22 | 4 | 100 |
| 23 | 8 | 1000 |
| 24 | 16 | 10000 |
| 25 | 32 | 100000 |
| 26 | 64 | 1000000 |
| 27 | 128 | 10000000 |
| 28 | 256 | 100000000 |
| 29 | 512 | 1000000000 |
| 210 | 1,024 | 10000000000 |
| 211 | 2,048 | 100000000000 |
| 212 | 4,096 | 1000000000000 |
| 213 | 8,192 | 10000000000000 |
| 214 | 16,384 | 100000000000000 |
| 215 | 32,768 | 1000000000000000 |
| 216 | 65,536 | 10000000000000000 |
| Binary | Decimal | Octal | Hexadecimal |
|---|---|---|---|
| 0000 | 0 | 0 | 0 |
| 0001 | 1 | 1 | 1 |
| 0010 | 2 | 2 | 2 |
| 0011 | 3 | 3 | 3 |
| 0100 | 4 | 4 | 4 |
| 0101 | 5 | 5 | 5 |
| 0110 | 6 | 6 | 6 |
| 0111 | 7 | 7 | 7 |
| 1000 | 8 | 10 | 8 |
| 1001 | 9 | 11 | 9 |
| 1010 | 10 | 12 | A |
| 1011 | 11 | 13 | B |
| 1100 | 12 | 14 | C |
| 1101 | 13 | 15 | D |
| 1110 | 14 | 16 | E |
| 1111 | 15 | 17 | F |
| Bits | Signed (two’s complement) | Unsigned |
|---|---|---|
| 8 | -128 to 127 | 0 to 255 |
| 16 | -32,768 to 32,767 | 0 to 65,535 |
| 32 | -2,147,483,648 to 2,147,483,647 | 0 to 4,294,967,295 |
| 64 | -9,223,372,036,854,775,808 to 9,223,372,036,854,775,807 | 0 to 18,446,744,073,709,551,615 |
Most online binary calculators stop at an answer. This one is built to explain it.
| Feature | This calculator | Typical basic calculator |
|---|---|---|
| Shows the working | Carries, borrows, partial products, a long-division table and place values | Often the final answer only |
| Division | Quotient and remainder, with the steps | Often a single result |
| Negative numbers | Minus sign or the plus-minus button, with the sign rules explained | Often unsupported or not explained |
| AND, OR, XOR, NOT and shifts | Same page, in 8, 16, 32 or 64 bits or an automatic width | Usually a separate tool |
| Two’s complement | Pick a width and see the pattern, the signed and unsigned values and any overflow | Usually a separate tool |
| Number length | Up to 4,096 digits, calculated exactly | Often a limit that is not stated |
| Updates | As you type, with no Calculate button | Some need a Calculate button |
| Reuse and sharing | Result becomes the next A in one tap, and a share link keeps your inputs | Rarely |
Work a problem by hand, then compare every carry, borrow and partial product with the steps shown here.
See how an adder carries from column to column, how AND, OR and XOR combine bits, and what overflow looks like in 8 bits.
Test a mask with AND, set a flag with OR, toggle one with XOR, and check which bits a shift drops before you write the code.
Check 8, 16, 32 and 64-bit values in binary, decimal, hexadecimal and octal side by side, with the two’s complement reading.
Applying a subnet mask to an address is a bitwise AND, so you can practise it one octet at a time with two 8-bit values.
Rehearse negative numbers in two’s complement and check long division with a remainder against a worked, step-by-step answer.
A few details explain most surprises. Binary is one of several ways to write a number: the Morse code translator shows another code, and the calculators page lists the rest of our calculators.
0001011 and 1011 are both 11. The result is shown without padding unless you choose a width or group the digits into nibbles or bytes.
The quotient is a whole number, cut toward zero, so -1101 ÷ 10 is -110 with remainder -1. The remainder takes the sign of A.
In 8 bits the signed range is -128 to 127. The most negative value has no positive twin, so negating -128 gives -128 again.
NOT 00110101 is 11001010 in 8 bits but has 32 digits in 32 bits. Auto picks the smallest of 8, 16, 24 bits and so on that fits your numbers.
A logical shift fills the left with zeros. An arithmetic shift copies the sign bit, so negative numbers stay negative and the result is rounded down.
Your browser does the maths and nothing is sent to a server. After the page has loaded it usually keeps working without a connection.
There are no binary fractions or floating-point numbers. For fractions written in decimal, the fraction calculator is the better fit.
Division returns a whole-number quotient and a remainder, so 1 ÷ 11 is 0 with remainder 1 rather than a binary point.
Each number can have up to 4,096 digits. Column working is shown up to 128 digits for add and subtract and 64 for multiply and divide, and the answer above it stays exact.
The rules and ranges on this page come from these references. The calculator follows them, and the examples above were checked by hand in decimal.
Short answers to what people ask most.
Add column by column from the right using 0 + 0 = 0, 0 + 1 = 1 and 1 + 1 = 10, which writes 0 and carries 1 into the next column. For example, 1011 + 110 = 10001, which is 11 + 6 = 17 in decimal.
Subtract column by column from the right. When a column needs 0 – 1, borrow a 1 from the column on its left, which is worth 2 in the column you are working on. For example, 1010 – 11 = 111, which is 10 – 3 = 7.
Write the first number shifted left once for every 1 in the second number, counting from the right, then add those rows. For example, 101 × 11 = 1111, which is 5 × 3 = 15.
Use long division: bring down bits one at a time, subtract the divisor whenever it fits and write a 1 in the quotient, otherwise write a 0. For example, 1101 ÷ 10 = 110 with remainder 1, which is 13 ÷ 2 = 6 remainder 1.
1 + 1 is 10 in binary, read as one-zero and not ten. It means 0 in the current column and a carry of 1 into the next column, and it equals 2 in decimal.
Multiply each digit by the power of two for its place, counting from 2^0 on the right, and add the results. For example, 10101010 is 128 + 32 + 8 + 2 = 170.
Divide the number by 2 again and again, write down each remainder, and read the remainders from last to first. For example, 170 gives the remainders 0, 1, 0, 1, 0, 1, 0, 1 from first to last, so the binary number is 10101010.
Two’s complement is the usual way computers store negative whole numbers in a fixed number of bits. To get the negative of a number, flip every bit and add 1, so 6 is 00000110 and -6 is 11111010 in 8 bits.
Signed two’s complement covers -128 to 127 in 8 bits, -32,768 to 32,767 in 16 bits and -2,147,483,648 to 2,147,483,647 in 32 bits. In 64 bits it covers -9,223,372,036,854,775,808 to 9,223,372,036,854,775,807, and unsigned numbers run from 0 up to 255, 65,535, 4,294,967,295 and 18,446,744,073,709,551,615.
AND gives 1 only where both bits are 1, OR gives 1 where at least one bit is 1, and XOR gives 1 where the bits differ. NOT flips every bit inside the chosen width, so NOT 00110101 is 11001010 in 8 bits.
Yes. Type a minus sign or tap the plus-minus button, and use up to 4,096 digits per number because the maths uses exact whole-number arithmetic. Division gives a whole-number quotient and a remainder, with no binary fractions.
No. This calculator does maths on binary numbers, while a binary translator turns letters and words into the binary codes of their characters. For text, use the binary translator or the binary to text converter on this site.