Two's Complement Calculator

How to use the Two's Complement Calculator

1. 1Enter a decimal number, or binary digits, and a bit width.
2. 2Pick the units or options from the menus if the two's complement tool offers them.
3. 3Read the two's complement in the large result box.
4. 4Look at the extra rows for related figures.
5. 5Press Copy result to keep the answer.

When you need the two's complement

Programmers, students of computer architecture and people debugging low-level code use it often. It makes clear why adding 1 to the biggest integer wraps round to the smallest.

A signed n-bit number covers −2ⁿ⁻¹ to 2ⁿ⁻¹ − 1, so there is one more negative value than positive. The top bit is the sign bit.

How the two's complement is worked out

For a negative number, the stored value is 2ⁿ plus the number, where n is the bit width. A bit pattern with the top bit set means a negative number, equal to the pattern minus 2ⁿ. −42 in 8 bits is 256 − 42 = 214, which is 11010110 in binary or D6 in hex. Reading 11010110 as an 8-bit number gives −42 again. An 8-bit number ranges from −128 to 127.

Every answer on this page comes from that one rule, so you can check any result by hand with a calculator. The figures shown underneath, such as other units, are conversions of the same answer.

• Both directions
• 4 to 64 bits
• Shows range

Mistakes to avoid with two's complement

Pick the bit width first: the same bits mean different numbers at 8 and 16 bits. A number outside the range cannot be stored, and the tool says so instead of silently wrapping.

On phone and computer

On a phone, type into the boxes one after another and read the two's complement underneath; Copy result puts it on the clipboard for a message or a note. On a computer the inputs sit on the left and the answer on the right, so you can change one figure and watch the two's complement move. The two's complement calculator works the same on both.

Checking your two's complement by hand

A good habit is to test the two's complement calculator with a case you already know. −42 in 8 bits is 256 − 42 = 214, which is 11010110 in binary or D6 in hex. Reading 11010110 as an 8-bit number gives −42 again. An 8-bit number ranges from −128 to 127.

If your own figures give a surprising answer, repeat the working yourself: For a negative number, the stored value is 2ⁿ plus the number, where n is the bit width. A bit pattern with the top bit set means a negative number, equal to the pattern minus 2ⁿ. Small differences usually come from rounding, from mixing units, or from a typing slip in one of the inputs. Signed numbers are stored in bits, so related tools help you read them. Write ones and zeros with the Binary Translator, do bit sums with the Binary and Hex Calculator, and see decimals stored as bits with the IEEE 754 Converter.

Features

• Pick the bit width first
• Out-of-range numbers cannot be stored
• The top bit is the sign
• Clear messages when the two's complement inputs make no sense
• Copy the result with one tap
• Private: nothing is uploaded

Frequently asked questions