Signed Numbers in Digital Electronics: Representation and Meaning
by Yuvi K - December 16, 2023
What are Signed Numbers in Digital Electronics?
Signed numbers in digital electronics refer to representations of numbers that contain a sign to indicate whether they are positive or negative. In the field of digital electronics, signed numbers are generally represented in two’s complement format. This is because two’s complement makes working with signed numbers much easier than any other format.
The signed numbers are numbers that are explicitly associated with a sign, either negative or positive. Signed numbers are usually represented in digital circuits by using the two’s complement form. This representation is used since it is simpler than any other format. In two’s complement, a number is represented in terms of its binary values, with a sign bit indicating either a positive or negative value.
Representation of Signed Numbers
The representation of a signed number in digital electronics is two’s complement. In two’s complement representation, the leftmost bit of a number is used as the sign bit. A sign bit of 0 denotes a positive number, and a sign bit of 1 denotes a negative number. The remaining bits are used to represent the magnitude (आकार) of the number.
For example, let’s consider the number 8 (eight). In two’s complement representation, 8 would be represented as 0000 1000. The leftmost bit, in this case, is 0, which denotes a positive number.
On the other hand, if the number is to be represented as -8 (minus eight), then it would be represented as 1000 1000 using two’s complement representation. The leftmost bit is a 1, which denotes a negative number.
Meaning of Signed Numbers
Signed numbers are used in digital electronics to represent values with a range between negative and positive values. For example, the two’s complement representation of a signed number can be used to store both positive and negative numbers in a digital circuit.
In two’s complement, negative numbers are represented as the two’s complement of the positive number. To find the negative number from a positive number, the bits of the positive number are inverted and then 1 is added to the result.
For example, -8 (minus eight) is represented as 1000 1000 in two’s complement. This can be calculated by inverting the bits of 8 (eight), which gives 1111 0111, and then adding 1 to this result, which gives 1000 1000.
Examples of Signed Numbers in Digital Electronics
Here are some examples of signed numbers represented in digital electronics:
| Number | Positive Representation | Negative Representation |
|---|---|---|
| +6 (six) | 0000 0110 | 1111 1010 |
| -4 (four) | 0000 0100 | 1111 1100 |
| +9 (nine) | 0000 1001 | 1111 0111 |
| -12 (twelve) | 0000 1100 | 1111 0011 |
Conclusion
In conclusion, signed numbers in digital electronics are represented in two’s complement format. This format is used because it is simpler than other formats and makes working with signed numbers much easier.
In two’s complement, a number is represented in terms of its binary values, with a sign bit indicating either a positive or negative value. Negative numbers are represented as the two’s complement of the positive number, which can be calculated by inverting the bits of the positive number and then adding 1 to the result.
Signed numbers are used in digital electronics to represent values with a range between negative and positive values. Therefore, it is important to understand how signed numbers are represented and how they work in digital electronics.
