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

123456789101112131415
??1?010?1101101

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

123456789101112131415
??1?101?1100001

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:

123456789101112131415
001011000110011

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)

123456789101112131415
010111101101100

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