Question

1. Give the signed decimal value of A93 (12 bits, show work)

Answer 1

-1389

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 A93 to binary
A => 1010
9 => 1001
3 => 0011
So, in binary A93 is 101010010011

Now converting A93 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.
   101010010011 is flipped to 010101101100
II. Add 1 to above result
010101101100 + 1 = 010101101101
III. Now convert this result to decimal value
Converting 10101101101 to decimal
10101101101
=> 1x2^10+0x2^9+1x2^8+0x2^7+1x2^6+1x2^5+0x2^4+1x2^3+1x2^2+0x2^1+1x2^0
=> 1x1024+0x512+1x256+0x128+1x64+1x32+0x16+1x8+1x4+0x2+1x1
=> 1024+0+256+0+64+32+0+8+4+0+1
=> 1389
Answer: -1389