c-gcc, 70 bytes

Result

WA

Code [DL]

main(s){for(;gets(&s);printf("%f",fmod(sqrt(strtol(&s,0,2)*8+1),1)));}

stdin

11111101
00000110
01111000
01101011
11111001
11100101
11010000
00001111
00000001
11110000
00011100
11101001
10100010
00010100
11100111
01011001
00011101
01100101
10011001
01110010
01000010
11111101
01001110
00000011
01101001
00100100
00101101
10110011
10001000
01101100
00001010
11000011
11000010
11010010
00111111
10101011
00011010
01011011
11010010
10111110
00000000
01000100
00110111
01110111
10111011
00010101
01111100
11110011
00110101
10110111

stdout

0.0000000.0000000.0000000.2745620.6430290.8135490.8044120.0000000.0000000.8292140.0000000.1856460.0138860.6885780.0000000.7020600.2643380.4429250.0000000.2158900.0000000.0000000.0000000.0000000.0000000.0000000.0000000.8549860.0000000.4108820.0000000.5094930.4081210.0000000.4722050.0000000.4568320.0000000.0000000.0000000.0000000.3452350.0000000.8706980.6910840.0000000.5119030.1021540.6155280.275318

stderr

/tmp/code.c:1:1: warning: return type defaults to ‘int’ [-Wimplicit-int]
 main(s){for(;gets(&s);printf("%f",fmod(sqrt(strtol(&s,0,2)*8+1),1)));}
 ^
/tmp/code.c: In function ‘main’:
/tmp/code.c:1:1: warning: type of ‘s’ defaults to ‘int’ [-Wimplicit-int]
/tmp/code.c:1:14: warning: implicit declaration of function ‘gets’ [-Wimplicit-function-declaration]
 main(s){for(;gets(&s);printf("%f",fmod(sqrt(strtol(&s,0,2)*8+1),1)));}
              ^
/tmp/code.c:1:23: warning: implicit declaration of function ‘printf’ [-Wimplicit-function-declaration]
 main(s){for(;gets(&s);printf("%f",fmod(sqrt(strtol(&s,0,2)*8+1),1)));}
                       ^
/tmp/code.c:1:23: warning: incompatible implicit declaration of built-in function ‘printf’
/tmp/code.c:1:23: note: include ‘<stdio.h>’ or provide a declaration of ‘printf’
/tmp/code.c:1:35: warning: implicit declaration of function ‘fmod’ [-Wimplicit-function-declaration]
 main(s){for(;gets(&s);printf("%f",fmod(sqrt(strtol(&s,0,2)*8+1),1)));}
                                   ^
/tmp/code.c:1:35: warning: incompatible implicit declaration of built-in function ‘fmod’
/tmp/code.c:1:35: note: include ‘<math.h>’ or provide a declaration of ‘fmod’
/tmp/code.c:1:40: warning: implicit declaration of function ‘sqrt’ [-Wimplicit-function-declaration]
 main(s){for(;gets(&s);printf("%f",fmod(sqrt(strtol(&s,0,2)*8+1),1)));}
                                        ^
/tmp/code.c:1:40: warning: incompatible implicit declaration of built-in function ‘sqrt’
/tmp/code.c:1:40: note: include ‘<math.h>’ or provide a declaration of ‘sqrt’
/tmp/code.c:1:45: warning: implicit declaration of function ‘strtol’ [-Wimplicit-function-declaration]
 main(s){for(;gets(&s);printf("%f",fmod(sqrt(strtol(&s,0,2)*8+1),1)));}
                                             ^
/tmp/ccNksZV4.o: In function `main':
code.c:(.text.startup+0x60): warning: the `gets' function is dangerous and should not be used.

strace