Advanced Mathematical Tutorial
How to Convert Signed Binary to Decimal.
An in-depth guide to signed binary representations: sign-magnitude, one's complement, and two's complement systems.
Try it: Signed 8-Bit Two's Complement Calculator
Signed Decimal Value: -3
What is a signed binary number?
In standard unsigned binary, all numbers are assumed to be positive. To represent negative values in hardware, computers use **signed binary systems**. The most common system is Two's Complement, though Sign-Magnitude and One's Complement also exist.
In all signed systems, the **Most Significant Bit (MSB)**—the leftmost digit—acts as the sign indicator. A 0 indicates a positive number, while a 1 indicates a negative number.
Two's complement conversion steps.
If the MSB of a binary number is 1 (meaning it is negative), use these steps to find its decimal value:
- Identify that the number is negative (leftmost bit is
1). - Invert all the bits: change
0to1and1to0. This is called taking the one's complement. - Add 1 to the inverted binary result.
- Convert the resulting binary value to decimal.
- Add a negative sign to the final decimal value.
Step-by-step example.
Convert the signed 8-bit binary number 11111101 to decimal:
• MSB is 1, so the number is negative.
• Invert the bits: 11111101 ➔ 00000010
• Add 1: 00000010 + 1 = 00000011
• Convert 00000011 to decimal: 3
• Add a negative sign: Result = -3
8-Bit Signed Examples
| Binary | Signed Dec |
|---|---|
| 01111111 | 127 (Max Pos) |
| 00000001 | 1 |
| 00000000 | 0 |
| 11111111 | -1 |
| 11111100 | -4 |
| 10000000 | -128 (Max Neg) |