[Hamming algorithm] having problems understanding the step highlighted in bold. explain the part going over checking the parity bits (the problem question is listed below)

12+1+r<=2^r-->r=5

5+12=17 for bit length-->

-->parity bits check positions are 1,2,4,8,16-->fill in the using BIN skipping over the 1,2,4,8,16 positions-->

-->

1=1

2=2

3=1+2

4=4

5=1+4

6=2+4

7=1+2+4

8=8

9=1+8

10=2+8

11=1+2+8

12=4+8

13=1+4+8

14=2+4+8

15=1+2+4+8

16=4+4+8

from my understanding, you check over the parity bits 1,2,4,8,16. using above as a reference. for bit 1 you look for each number that contains a 1 and for bit 2 you look for each number that contains a 2.

for 1: 1,3,5,7,9,11,15,17=1

for 2: 2,3,6,7,10,11,14,15 =1

how do you determine those are 1s from that?

it would look like so far 1_001 0001 _101 _0_11

Assuming we are using the Hamming algorithm presented in our text to design an error-correcting code, find the code word to represent the 12-bit information word 1001 0001 1010

a. 1 1001 0001 0101 1011 b. 1 1001 0001 1101 1001 c. 1 1001 0001 1101 1011 d. 1 0001 0001 0101 1011