Question

Question 1: (4 pts) (CLO#: 4 )(SO#: 1) [1]. The hex number 8f is Unsigned decimal number ..... Signed decimal number using 2's complement :...... (2). Using 10-bit representation : Give your answer in decimal (i) The largest unsigned value is : .......... (ii) The smallest unsigned value is: ................ (ii) The largest signed value is ... (iii) The smallest negative signed value is: ................

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 8F to binary
8 => 1000
F => 1111
So, in binary 8F is 10001111

a)
Converting 10001111 to decimal
10001111
=> 1x2^7+0x2^6+0x2^5+0x2^4+1x2^3+1x2^2+1x2^1+1x2^0
=> 1x128+0x64+0x32+0x16+1x8+1x4+1x2+1x1
=> 128+0+0+0+8+4+2+1
=> 143
Answer: 143

b)
10001111
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.
   10001111 is flipped to 01110000
II. Add 1 to above result
01110000 + 1 = 01110001
III. Now convert this result to decimal value
Converting 1110001 to decimal
1110001
=> 1x2^6+1x2^5+1x2^4+0x2^3+0x2^2+0x2^1+1x2^0
=> 1x64+1x32+1x16+0x8+0x4+0x2+1x1
=> 64+32+16+0+0+0+1
=> 113
Answer: -113

2)
a)
2^10 - 1
= 1024 - 1
= 1023
Answer: 1023

b)
Answer: 0

c)
2^9 - 1
= 512 - 1
= 511
Answer: 511

d)
-2^9
= -512
Answer: -512