Binary Representation of Numbers in Computer Systems
How are numbers represented in computer systems using different signed representations?
What are the 16-bit signed representations of 217 and -217 using Signed Magnitude, One's Complement, and Two's Complement systems?
Answer:
The 16-bit signed representations of 217 and -217 are different in signed magnitude, one's complement, and two's complement systems. For 217, the representations are:
Signed Magnitude (0000 1101 1001 1001), One's Complement (0000 1101 1001 1001), and Two's Complement (0000 1101 1001 1001).
For -217, they become: Signed Magnitude (1000 1101 1001 1001), One's Complement (1111 0010 0110 0110), and Two's Complement (1111 0010 0110 0111).
To represent the decimals 217 and -217 in 16-bit signed representations, we will use signed magnitude, one's complement, and two's complement systems. These systems are used in computers to represent positive and negative numbers using binary codes. Here's how the representations work:
- Signed Magnitude: The first bit is the sign bit (0 for positive and 1 for negative), and the remaining bits represent the magnitude of the number. For 217, the positive representation is straightforward, while for -217, the sign bit is inverted to indicate negativity.
- One's Complement: In this system, all bits are inverted (flipped) to represent a negative number. For -217, all the bits of the positive representation of 217 are flipped to get the one's complement representation.
- Two's Complement: To get the two's complement representation of a negative number, invert all bits of the positive representation and then add 1. This system allows for easy addition and subtraction of numbers in binary form.