Perform the 8-bit two's complement binary sum 17 - 24

The first step is to view the sum as an addition of a positive and a negative number, rather than a subtraction:
17 + (-24)
 
From there we can work out the binary equivalents of the 2 numbers:
     b7 b6 b6 b4 b3 b2 b1 b0
17   0  0  0  1  0  0  0  1
24   0  0  0  1  1  0  0  0
 
24 then has to be converted into it's equivalent negative number in two's complement. This is done in 2 steps:
1. Flip all the bits in the number
2. Peform binary addition of new number and 1.
 
So first we flip all the bits:
b7 b6 b6 b4 b3 b2 b1 b0
1  1  1  0  0  1  1  1
 
Then we add 1:
b7 b6 b6 b4 b3 b2 b1 b0
1  1  1  0  0  1  1  1
0  0  0  0  0  0  0  1
1  1  1  0  1  0   0   0
This gives us the two's complement representation of -24.
 
Then we simply perform the additon of 17 and -24 in binary:
b7 b6 b6 b4 b3 b2 b1 b0
0  0  0  1  0  0  0  1
1  1  1  0  1  0  0  0
1  1  1  1  1  0  0  1
 
Which, as expected, is the binary representation of -7 (you can check this by performing the same 2 stage method to convert the number back to positive 7, then back into decimal from there).