About the Decimal/Two’s Complement Converter
This is a decimal to two’s complement converter and a two’s complement to decimal converter. These converters do not complement their input; that is, they do not negate it. They just convert it to or from two’s complement form. For example, -7 converts to 11111001 (to 8 bits), which is -7 in two’s complement. (Complementing it would make it 7, or 00000111 to 8 bits.) Similarly, 0011 converts to 3, not -3.
How to Use the Decimal/Two’s Complement Converter
Decimal to Two’s Complement
- Enter a positive or negative integer.
- Set the number of bits for the two’s complement representation (if different than the default).
- Click ‘Convert’ to convert.
- Click ‘Clear’ to reset the form and start from scratch.
If you want to convert another number, just type over the original number and click ‘Convert’ — there is no need to click ‘Clear’ first.
If the number you enter is too big to be represented in the requested number of bits, you will get an error message telling you so (it will tell you how many bits you need).
Two’s Complement to Decimal
- Enter a two’s complement number — a string of 0s and 1s.
- Set the number of bits to match the length of the input (if different than the default).
- Click ‘Convert’ to convert.
- Click ‘Clear’ to reset the form and start from scratch.
The output will be a positive or negative decimal number.
Exploring Properties of Two’s Complement Conversion
The best way to explore two’s complement conversion is to start out with a small number of bits. For example, let’s start with 4 bits, which can represent 16 decimal numbers, the range -8 to 7. Here’s what the decimal to two’s complement converter returns for these 16 values:
| Decimal Number | Two’s Complement |
|---|---|
| -8 | 1000 |
| -7 | 1001 |
| -6 | 1010 |
| -5 | 1011 |
| -4 | 1100 |
| -3 | 1101 |
| -2 | 1110 |
| -1 | 1111 |
| 0 | 0000 |
| 1 | 0001 |
| 2 | 0010 |
| 3 | 0011 |
| 4 | 0100 |
| 5 | 0101 |
| 6 | 0110 |
| 7 | 0111 |
Nonnegative integers always start with a ‘0’, and will have as many leading zeros as necessary to pad them out to the required number of bits. (If you strip the leading zeros, you’ll get the pure binary representation of the number.) Negative integers always start with a ‘1’.
If you run those two’s complement values through the two’s complement to decimal converter, you will confirm that the conversions are correct. Here is the same table, but listed in binary lexicographical order:
| Two’s Complement | Decimal Number |
|---|---|
| 0000 | 0 |
| 0001 | 1 |
| 0010 | 2 |
| 0011 | 3 |
| 0100 | 4 |
| 0101 | 5 |
| 0110 | 6 |
| 0111 | 7 |
| 1000 | -8 |
| 1001 | -7 |
| 1010 | -6 |
| 1011 | -5 |
| 1100 | -4 |
| 1101 | -3 |
| 1110 | -2 |
| 1111 | -1 |
No matter how many bits you use in your two’s complement representation, -1 decimal is always a string of 1s in binary.