vim, 39 bytes

Result

WA

Code [DL]

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

Disassembly

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

stdin

00110111
00101011
00010101
11000001
00110111
11010001
00000001
10001101
10101001
00010000
01000111
11101100
00101111
01101001
11010010
01000010
00011100
00101101
10001000
10000111
10101011
01001110
10110110
00100100
10110100
00000000
11100111
01001011
00001111
10111110
00000110
01111000
11110111
10001000
00011001
00000011
10000011
10100110
11111101
11000100
11000010
10101000
11111000
10001010
10100100
01100001
01110100
00001010
10011001
01011011

stdout

00110111
00101011
00010101
11000001
00110111
11010001
00000001
10001101
10101001
00010000
01000111
11101100
00101111
01101001
11010010
01000010
00011100
00101101
10001000
10000111
10101011
01001110
10110110
00100100
10110100
00000000
11100111
01001011
00001111
10111110
00000110
01111000
11110111
10001000
00011001
00000011
10000011
10100110
11111101
11000100
11000010
10101000
11111000
10001010
10100100
01100001
01110100
00001010
10011001
01011011

stderr

strace