Attach an even-parity bit to each of the ASCII codes for Problem 2-24, and give the results in hex.
The correct answer and explanation is :
To answer this question, we’ll first clarify the steps involved in solving Problem 2-24, which typically involves computing ASCII codes and attaching an even-parity bit. Although the actual content of Problem 2-24 isn’t provided here, it usually includes a set of characters whose ASCII codes are to be used.
Let’s assume Problem 2-24 gives you a string of characters like:
“DOG”
We will compute the 7-bit ASCII codes for each character, attach an even parity bit to the left (as the most significant bit), and present the 8-bit results in hexadecimal.
Step-by-step:
1. Get ASCII codes (7-bit binary):
- D: ASCII = 68 → 1000100
- O: ASCII = 79 → 1001111
- G: ASCII = 71 → 1000111
2. Compute even parity bit:
Even parity means the total number of 1s (including the parity bit) must be even.
- D (1000100) has 2 ones → already even → parity bit = 0
→ Final 8 bits: 01000100 → Hex: 0x44 - O (1001111) has 5 ones → odd → need one more 1 → parity bit = 1
→ Final 8 bits: 11001111 → Hex: 0xCF - G (1000111) has 4 ones → already even → parity bit = 0
→ Final 8 bits: 01000111 → Hex: 0x47
Final Results with Even Parity Bits (in Hex):
- D →
0x44 - O →
0xCF - G →
0x47
Explanation (Approx. 300 words):
The concept of parity bits is foundational in digital communication and error detection. A parity bit is a single binary digit added to a binary string to ensure the number of bits with the value “1” is even (even parity) or odd (odd parity). In this question, we focus on even parity.
ASCII characters are typically represented using 7 bits. When adding a parity bit, we extend this to 8 bits. For even parity, if the original 7 bits contain an odd number of ones, we set the parity bit to 1 to make the total count even. If the 7 bits already have an even number of ones, we set the parity bit to 0.
In our example, we processed the string “DOG”, found the binary ASCII representations, and calculated the parity bit for each. The parity bit was prepended (placed at the most significant bit position), converting each 7-bit code to an 8-bit value. We then converted each of these 8-bit binary strings to hexadecimal for compactness.
Even parity is widely used in communication protocols like RS-232 and in memory systems where simple error checking is adequate. While not foolproof (it can’t detect even-numbered bit errors), it adds a basic level of integrity checking with minimal overhead.