Question

3:40 PM Wed Jul 1 @ 47% + : 0 show all work! 0 X 4279 d. OxFFFF - E = (base-16) = (base-2) Hint: If E = 0x8000, then OxFFFF-Ox8000 = 0x7FFF unsigned short: short:

Answer 1

0xFFFF - 0x4279
= 0xBD86 (base-16) = 1011110110000110 (base-2)
unsigned short: 48518
short:  -17018

Explanation:
-------------
0xFFFF - 0x4279
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 FFFF to binary
F => 1111
F => 1111
F => 1111
F => 1111
So, in binary FFFF is 1111111111111111

Converting 4279 to binary
4 => 0100
2 => 0010
7 => 0111
9 => 1001
So, in binary 4279 is 0100001001111001

subtracting these two binary numbers
1111111111111111
0100001001111001
-----------------
1011110110000110
-----------------

convert this back to hexadecimal
1011 => B
1101 => D
1000 => 8
0110 => 6
So, in hexadecimal 1011110110000110 is 0xBD86

unsigned:
----------
Converting 1011110110000110 to decimal
1011110110000110
=> 1x2^15+0x2^14+1x2^13+1x2^12+1x2^11+1x2^10+0x2^9+1x2^8+1x2^7+0x2^6+0x2^5+0x2^4+0x2^3+1x2^2+1x2^1+0x2^0
=> 1x32768+0x16384+1x8192+1x4096+1x2048+1x1024+0x512+1x256+1x128+0x64+0x32+0x16+0x8+1x4+1x2+0x1
=> 32768+0+8192+4096+2048+1024+0+256+128+0+0+0+0+4+2+0
Answer: 48518

signed:
---------
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.
   1011110110000110 is flipped to 0100001001111001
II. Add 1 to above result
0100001001111001 + 1 = 0100001001111010
III. Now convert this result to decimal value
Converting 100001001111010 to decimal
100001001111010
=> 1x2^14+0x2^13+0x2^12+0x2^11+0x2^10+1x2^9+0x2^8+0x2^7+1x2^6+1x2^5+1x2^4+1x2^3+0x2^2+1x2^1+0x2^0
=> 1x16384+0x8192+0x4096+0x2048+0x1024+1x512+0x256+0x128+1x64+1x32+1x16+1x8+0x4+1x2+0x1
=> 16384+0+0+0+0+512+0+0+64+32+16+8+0+2+0
=> 17018
Answer: -17018