Question

Give the signed decimal value of D03 (12 bits, show work)

Answer 1

-765

Explanation:
-------------
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 hexadecimal to binary
Converting D03 to binary
D => 1101
0 => 0000
3 => 0011
So, in binary D03 is 110100000011

Now converting D03 to decimal
since left most bit is 1, this number is negative number.
so, follow these steps below to convert this into a decimal value.
I. first flip all the bits. Flip all 0's to 1 and all 1's to 0.
   110100000011 is flipped to 001011111100
II. Add 1 to above result
001011111100 + 1 = 001011111101
III. Now convert this result to decimal value
Converting 1011111101 to decimal
1011111101
=> 1x2^9+0x2^8+1x2^7+1x2^6+1x2^5+1x2^4+1x2^3+1x2^2+0x2^1+1x2^0
=> 1x512+0x256+1x128+1x64+1x32+1x16+1x8+1x4+0x2+1x1
=> 512+0+128+64+32+16+8+4+0+1
=> 765
Answer: -765