A. 11011111
To convert -33 to a signed binary number, a 2's complement representation of the number is used. Signed numbers are stored on the computer using 2's complement notation.
(i) First convert 33 to binary
2 | 33
2 | 16 r 1
2 | 8 r 0
2 | 4 r 0
2 | 2 r 0
2 | 1 r 0
2 | 0 r 1
Therefore writing the remainders from bottom to top, we have that
33 in binary is 100001
(ii) Since the options are all in 8 bits, convert the binary to its 8-bit representation by padding it with zeros(0s) at the left.
=> 100001 = 00100001
(iii) Now, convert to 2's complement by
(a) flipping all the bits in the binary number. i.e change all 1s to 0s and all 0s to 1s
=> 00100001 => 11011110
(b) and then adding 1 to the result as follows;
1 1 0 1 1 1 1 0
+ 1
1 1 0 1 1 1 1 1
Therefore, -33 to binary is 11011111
Hope this helps!
