Question

Please explain how you got the answers for signed and unsigned integer please and thank you!

OxFADE 13. Convert signed integer a. binary b. decimal 14. Convert unsigned integer OxFADE a. binary b. decimal

Answer 1

Answer

13)
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

a)
Converting FADE to binary
F => 1111
A => 1010
D => 1101
E => 1110
So, in binary FADE is 1111101011011110
Answer: 1111101011011110

b)
Now converting 0xFADE to decimal
1111101011011110
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.
   1111101011011110 is flipped to 0000010100100001
II. Add 1 to above result
0000010100100001 + 1 = 0000010100100010
III. Now convert this result to decimal value
Converting 10100100010 to decimal
10100100010
=> 1x2^10+0x2^9+1x2^8+0x2^7+0x2^6+1x2^5+0x2^4+0x2^3+0x2^2+1x2^1+0x2^0
=> 1x1024+0x512+1x256+0x128+0x64+1x32+0x16+0x8+0x4+1x2+0x1
=> 1024+0+256+0+0+32+0+0+0+2+0
=> 1314
Answer: -1314

14)
a)
Converting FADE to binary
F => 1111
A => 1010
D => 1101
E => 1110
So, in binary FADE is 1111101011011110
Answer: 1111101011011110

b)
FADE
=> Fx16^3+Ax16^2+Dx16^1+Ex16^0
=> Fx4096+Ax256+Dx16+Ex1
=> 15x4096+10x256+13x16+14x1
=> 61440+2560+208+14
=> 64222
Answer: 64222

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