Represent the statement “X = 3 × Y” in ASCII code. Attach an odd parity bit.
The correct answer and explanation is :
ASCII Representation with Odd Parity Bit: “X = 3 × Y”
Step 1: Convert each character to ASCII (7-bit binary)
The string is:
“X = 3 × Y” (7 characters, including spaces)
| Character | ASCII (Decimal) | ASCII (7-bit Binary) |
|---|---|---|
| X | 88 | 1011000 |
| 32 (space) | 0100000 | |
| = | 61 | 0111101 |
| 32 (space) | 0100000 | |
| 3 | 51 | 0110011 |
| × | 215 | 11010111 (8-bit) → Not ASCII standard |
| Y | 89 | 1011001 |
Note: ‘×’ (multiplication sign) is not in standard ASCII (which is 7-bit). It’s an extended ASCII character with code 215, binary:
11010111. But for simplicity, we will include its 8-bit form and apply parity accordingly.
Step 2: Add Odd Parity Bit (making total 8 bits)
Odd parity means the total number of 1s (including the parity bit) must be odd.
| Character | 7/8-bit Binary | # of 1s | Parity Bit | 8-bit w/ Odd Parity |
|---|---|---|---|---|
| X | 1011000 | 3 | 0 | 01011000 |
| (space) | 0100000 | 1 | 0 | 00100000 |
| = | 0111101 | 5 | 0 | 00111101 |
| (space) | 0100000 | 1 | 0 | 00100000 |
| 3 | 0110011 | 4 | 1 | 10110011 |
| × | 11010111 | 6 | 1 | 111010111 |
| Y | 1011001 | 4 | 1 | 11011001 |
Note: For standard ASCII characters, parity bit is prepended. For the 8-bit extended character (×), we prepend the parity bit to make 9 bits.
Final Binary (ASCII with Odd Parity) Output
01011000 (X)
00100000 (space)
00111101 (=)
00100000 (space)
10110011 (3)
111010111 (×)
11011001 (Y)Explanation (≈300 words)
The string “X = 3 × Y” consists of seven characters. Each character is represented in ASCII code, which uses a 7-bit binary number in its standard form. The purpose of converting characters into ASCII binary is to allow them to be transmitted or stored in digital systems like computers and communication devices.
To ensure the accuracy of data during transmission, parity bits are often used for error detection. A parity bit is a single bit added to a binary number to make the total number of 1s either even (even parity) or odd (odd parity). In this case, we’re instructed to use odd parity, which means that each 8-bit result must contain an odd number of 1s.
For instance, the ASCII for ‘X’ is 1011000, which contains 3 ones (already odd), so we add a 0 at the front to keep the total odd. On the other hand, the character ‘3’ in ASCII is 0110011, which contains 4 ones (even), so we prepend a 1 to make the total five (odd).
A complication arises with the character ‘×’ (multiplication sign). It is not part of the original 7-bit ASCII set, but rather belongs to extended ASCII, which uses 8 bits. We treat it as 8-bit binary 11010111. It contains 6 ones, which is even, so we add a 1 in front to make it 9 bits with 7 ones (odd).
This process ensures that every byte (or 9 bits in the × case) has an odd number of 1s, allowing receivers to check for single-bit transmission errors.