Question

construct hamming code for the message (1001)

Consider even parity

2p ≥ p+m+1

Answer 1

Given message is (1001)

Here the number of parits bits are 3 because When no of bits in message  m= 4

2^p >= p+4+1 =p+5

when 2^p >= p+ 5 , p should be 3

Therefore p = 3

So, now to transmit 4 bit message we require atleast 3 parity bits.

1	2	3	4	5	6	7
p1	p2	m1	p3	m2	m3	m4
p1	p2	1	p3	0	0	1

p1-> check 1,3,5,7 for even parity = p1101

here to make this even parity p1 must be 0, so p1 = 0

p2-> check 2,3,6,7 for even parity = p2101

here to make this even parity p2 must be 0, so p2 = 0

p3-> check 4,5,6,7 for even parity = p3001

here to make this even parity p3 must be 1, So p3= 1

Now replace the p1,p2,p3 with the above results.

p1	p2	m1	p3	m2	m3	m4
0	0	1	1	0	0	1

Therefore our required hamming code is 0011001

(If you still have any doubts regarding this answer please comment I will definitely help)