Question

if hexadecimal number FA16 represent a signed number in signed magnitude, what the decimal representation of that number? include the sign for that number with no spaces between the number and sign. for example -3 or +3

Answer 1

-122

Explanation:
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Let's first convert FA to binary
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 FA to binary
F => 1111
A => 1010
So, in binary FA is 11111010

Now, let's convert 11111010 to one's complement decimal
Left most bit is 1. so, it's negative.
Now, let's convert rest of the bits 1111010 to decimal
Converting 1111010 to decimal
1111010
=> 1x2^6+1x2^5+1x2^4+1x2^3+0x2^2+1x2^1+0x2^0
=> 1x64+1x32+1x16+1x8+0x4+1x2+0x1
=> 64+32+16+8+0+2+0
=> 122
so, 11111010 from sign-magnitude to decimal is -122