vim, 41 bytes

Result

WA

Code [DL]

:%s/.*/\=sqrt(("0b".submatch(0))*8+1)/
ZZ

Disassembly

:%s/.*/\=sqrt(("0b".submatch(0))*8+1)/<NL>ZZ

stdin

10111001
01001011
01011101
00000001
01111111
11010010
11011011
10001000
10011001
11100111
10000101
10001110
01000010
00010101
00011100
00000110
00111111
10000000
10111110
11110010
10101011
10111011
00110111
00100100
00100000
10011010
00001001
00100110
01011011
01010111
00001010
00000110
11111000
00111101
11111101
00000000
00000011
01110110
00000110
01101110
01101001
11010001
01111000
11101001
00100111
01001111
00101101
00001111
01111010
01001110

stdout

38.483763
24.515301
27.294688
3.0
31.890437
41.0
41.868843
33.0
35.0
43.0
32.634338
33.719431
23.0
13.0
15.0
7.0
22.472205
32.015621
39.0
44.011362
37.0
38.691084
21.0
17.0
16.03122
35.1141
8.544004
17.464249
27.0
26.400758
9.0
7.0
44.553339
22.113344
45.0
1.0
5.0
30.740852
7.0
29.681644
29.0
40.902323
31.0
43.185646
17.691806
25.159491
19.0
11.0
31.256999
25.0

stderr

strace