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Consider all possible 4-bit datawords (There will be 16). For each dataword, fin

ID: 3733677 • Letter: C

Question

Consider all possible 4-bit datawords (There will be 16). For each dataword, find the single bit parity to form the 5-bit codeword. What is the Hamming distance for the code set thus obtained? How many bit errors can this codeset detect? What is the number of legal and illegal codewords? Consider all possible 4-bit datawords (There will be 16). For each dataword, find the single bit parity to form the 5-bit codeword. What is the Hamming distance for the code set thus obtained? How many bit errors can this codeset detect? What is the number of legal and illegal codewords?

Explanation / Answer

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Possible 5-bit

combos codeword

1) 0000 00000

2) 0001 00011

3) 0010 00101

4) 0011 00110

5) 0100 01001

6) 0101 01010

7) 0110 01100

8) 0111 01111

9) 1000 10001

10) 1001 10010

11) 1010 10100

12) 1011 10111

13) 1100 11000

14) 1101 11011

15) 1110 11101

16) 1111 11110

Min hamming distance for this set is 2 as any 2 set

like 01001 and 01010 differ at two places.

It can detect (d-1) bit errors, where d is hamming distance, hence it can detect 1 bit error.

In memory cell 2^4 i.e. 16 bits are legal out of 2^5 i.e 32 bits, hence 16 bits are illegal.