Question

Convert signed integer 0xACE9 to binary and decimal.

Convert unsigned integer0xACE9 to binary and decimal.

Answer 1

1)
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 ACE9 to binary
A => 1010
C => 1100
E => 1110
9 => 1001
So, in binary ACE9 is 1010110011101001
Answer in binary: 1010110011101001

=> 1010110011101001
=> 1x2^15+0x2^14+1x2^13+0x2^12+1x2^11+1x2^10+0x2^9+0x2^8+1x2^7+1x2^6+1x2^5+0x2^4+1x2^3+0x2^2+0x2^1+1x2^0
=> 1x32768+0x16384+1x8192+0x4096+1x2048+1x1024+0x512+0x256+1x128+1x64+1x32+0x16+1x8+0x4+0x2+1x1
=> 32768+0+8192+0+2048+1024+0+0+128+64+32+0+8+0+0+1
=> 44265
Answer in decimal: 44265

2)
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 ACE9 to binary
A => 1010
C => 1100
E => 1110
9 => 1001
So, in binary ACE9 is 1010110011101001
Answer in binary: 1010110011101001

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.
   1010110011101001 is flipped to 0101001100010110
II. Add 1 to above result
0101001100010110 + 1 = 0101001100010111
III. Now convert this result to decimal value
=> 101001100010111
=> 1x2^14+0x2^13+1x2^12+0x2^11+0x2^10+1x2^9+1x2^8+0x2^7+0x2^6+0x2^5+1x2^4+0x2^3+1x2^2+1x2^1+1x2^0
=> 1x16384+0x8192+1x4096+0x2048+0x1024+1x512+1x256+0x128+0x64+0x32+1x16+0x8+1x4+1x2+1x1
=> 16384+0+4096+0+0+512+256+0+0+0+16+0+4+2+1
=> 21271
Answer in decimal: -21271