vim, 65 bytes

Result

WA

Code [DL]

:exe ':%s/.\+/\=!(float2nr(sqrt(("0b".submatch(0))*8+1)*99)%99)/'

Disassembly

:exe ':%s/.\+/\=!(float2nr(sqrt(("0b".submatch(0))*8+1)*99)%99)/'

stdin

00000101
00001010
01010101
00011100
01011011
00010101
00100100
00100110
00110111
11101011
10001011
11111111
11001101
11111010
00000011
01001110
01000100
10100011
10101000
10101011
00001111
00101101
00000110
11100111
01000010
11010010
11110111
10010111
00100011
10011001
00000000
11101101
10000000
01101111
01101001
00000001
11101110
10111110
00101011
11000011
10000011
01100110
01111000
10001000
01110001
11111101
11010010
01001101
00001111
00010100

stdout

00000101
00001010
01010101
00011100
01011011
00010101
00100100
00100110
00110111
11101011
10001011
11111111
11001101
11111010
00000011
01001110
01000100
10100011
10101000
10101011
00001111
00101101
00000110
11100111
01000010
11010010
11110111
10010111
00100011
10011001
00000000
11101101
10000000
01101111
01101001
00000001
11101110
10111110
00101011
11000011
10000011
01100110
01111000
10001000
01110001
11111101
11010010
01001101
00001111
00010100

stderr

strace