Question

What is the 11 bit, binary representation of -108? What is the hexadecimal equivalent of this number?

Answer 1

Answer in binary:       11110010100
Answer in hexadecimal:  0x794

Explanation:
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-108
This is negative. so, follow these steps to convert this into a 2's complement binary
Step 1:
Divide 108 successively by 2 until the quotient is 0
   > 108/2 = 54, remainder is 0
   > 54/2 = 27, remainder is 0
   > 27/2 = 13, remainder is 1
   > 13/2 = 6, remainder is 1
   > 6/2 = 3, remainder is 0
   > 3/2 = 1, remainder is 1
   > 1/2 = 0, remainder is 1
Read remainders from the bottom to top as 1101100
So, 108 of decimal is 1101100 in binary
So, 108 in normal binary is 00001101100
Step 2: flip all the bits. Flip all 0's to 1 and all 1's to 0.
   00001101100 is flipped to 11110010011
Step 3:. Add 1 to above result
11110010011 + 1 = 11110010100
so, -108 in 2's complement binary is 11110010100

Adding 1 zeros on left hand side of this number to make it's length a multiple of 4
Hexadecimal     Binary
    0           0000
    1           0001
    2           0010
    3           0011
    4           0100
    5           0101
    6           0110
    7           0111
    8           1000
    9           1001
    A           1010
    B           1011
    C           1100
    D           1101
    E           1110
    F           1111
Use this table to convert from binary to hexadecimal
Converting 011110010100 to hexadecimal
0111 => 7
1001 => 9
0100 => 4
So, in hexadecimal 011110010100 is 0x794