Realize the code converter which converts the binary (BCD) code into the Hamming code as specified in Table 6.4.
The Correct Answer and Explanation is :
onverting Binary-Coded Decimal (BCD) to Hamming code involves encoding each decimal digit, represented in BCD, into a Hamming codeword.CD represents each decimal digit with a 4-bit binary number, while Hamming codes are error-correcting codes that add redundancy to detect and correct errors in data transmission.
Understanding BCD:
CD encodes each decimal digit (0-9) as a 4-bit binary number.For example:
Decimal 0: 0000- Decimal 1: 0001- Decimal 2: 0010- Decimal 3: 0011- Decimal 4: 0100- Decimal 5: 0101- Decimal 6: 0110- Decimal 7: 0111- Decimal 8: 1000- Decimal 9: 1001
Understanding Hamming Code:
amming codes are error-correcting codes that add parity bits to data bits to detect and correct single-bit errors.or a 4-bit data input, a 7-bit Hamming code is commonly used, which includes 3 parity bits.he positions of the parity bits are powers of two (1, 2, and 4), and the data bits occupy the remaining positions.
Converting BCD to Hamming Code:
o convert a 4-bit BCD digit to a 7-bit Hamming code:. Identify Data and Parity Bits: – Data bits (D): Positions 3, 5, 6, and 7 – Parity bits (P): Positions 1, 2, and 4. Assign Data Bits: Place the 4 BCD bits into the data bit positions.. Calculate Parity Bits: – P1 covers positions 1, 3, 5, and 7. Set P1 to 1 if the number of 1s in these positions is odd; otherwise, set it to 0. – P2 covers positions 2, 3, 6, and 7. Set P2 to 1 if the number of 1s in these positions is odd; otherwise, set it to 0. – P4 covers positions 4, 5, 6, and 7. Set P4 to 1 if the number of 1s in these positions is odd; otherwise, set it to 0.. Construct the Hamming Code: Combine the parity bits and data bits to form the 7-bit Hamming codeword.
Example:
onsider the BCD digit for decimal 5, which is 0101.. Assign Data Bits: – D1 = 0 – D2 = 1 – D3 = 0 – D4 = 1. Calculate Parity Bits: – P1 covers positions 1, 3, 5, and 7: P1 = 0 (even number of 1s) – P2 covers positions 2, 3, 6, and 7: P2 = 1 (odd number of 1s) – P4 covers positions 4, 5, 6, and 7: P4 = 0 (even number of 1s). Construct the Hamming Code: – Hamming codeword: P1 P2 D1 P4 D2 D3 D4 – Hamming codeword: 0 1 0 0 1 0 1
herefore, the 7-bit Hamming code for the BCD digit 0101 (decimal 5) is 0100101.
his process ensures that each 4-bit BCD digit is represented by a 7-bit Hamming code, allowing for error detection and correction in data transmission.
For a visual demonstration of constructing a Hamming code for a BCD digit, you can refer to the following video:
videoConstruction of Hamming Code for BCD 0110turn0search6