Fill in the syndrome bits for the following 11-bit messages:

1	2	3	4	5	6	7	8	9	10	11	12	13	14	15
?	?	1	?	0	1	0	?	1	1	0	1	1	0	1

a=0,b=0,c=0,d=1

1	2	3	4	5	6	7	8	9	10	11	12	13	14	15
?	?	1	?	1	0	1	?	1	1	0	0	0	0	1

a=1,b=0,c=1,d=1

Calculate the 4-bit syndromes from the following messages and find the single bit errors in each of them:

1	2	3	4	5	6	7	8	9	10	11	12	13	14	15
0	0	1	0	1	1	0	0	0	1	1	0	0	1	1

a = (1+3+5+7+9+11+13+15) % 2 = 1
b = (2+3+6+7+10+11+14+15) % 2 = 1
c = (4+5+6+7+12+13+14+15) % 2 = 1
d = (8+9+10+11+12+13+14+15) % 2 = 0

Actual syndrome, after error = dcba = 0111 = 7 (Error position=7)

1	2	3	4	5	6	7	8	9	10	11	12	13	14	15
0	1	0	1	1	1	1	0	1	1	0	1	1	0	0

Actual syndrome (after error) = dcba = 0001 = 1 (Error position=1)