Write the of the number 314159 as 4digit binary digits and e

Write the of the number 3.14159 as 4-digit binary digits and encode each of them using Hamming\'s [7, 4]-code. The following message was encoded using Hamming\'s 17, 4- code. Locate all errors and correct them: 1001011, 0101111, 1101001, 1110010. If I haven\'t done anything stupid, these are binary expansions of the decimal digits of e.

Solution

The 4 digit binary decimal of 3.14159 is 0011

1 2 3 4
0 0 1 1

part1 = B1+B2+B4 = 0+0+1 = 1
part2 = B1+B3+B4 = 0+1+1 = 2
part3 = B2+B3+B4 = 0+1+1 = 2

Hammimgs Code

P1 p2 B1 P3 B2 B3 B4
1 0 0 0 0 1 1

1001011 = 0011 no error
0101111 = 0111 no error
1101001 = 0001 no error
1110010 = 1010 no error