Question

I need clear explanation on how we got that answers. Thanks.

1. What is the decimal value for the 8 bit 2's complement number 0x36 arithmetic shift right by 3.

--> Ans is 6

2. What is the decimal value for the 8 bit 2's complement number 0x36 rotated left by 3

--> Ans is -79

Answer 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 36  to binary
3 => 0011
6 => 0110
So, in binary 36  is 00110110

1)
00110110 shifted right by 3 gives 00000110
since left most bit is 0, this number is positive
so, we can directly convert this into a decimal value
Converting 110 to decimal
110
=> 1x2^2+1x2^1+0x2^0
=> 1x4+1x2+0x1
=> 4+2+0
=> 6
Answer: 6

2)
00110110 shifted left by 3 gives 10110001
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.
   10110001 is flipped to 01001110
II. Add 1 to above result
01001110 + 1 = 01001111
III. Now convert this result to decimal value
Converting 1001111 to decimal
1001111
=> 1x2^6+0x2^5+0x2^4+1x2^3+1x2^2+1x2^1+1x2^0
=> 1x64+0x32+0x16+1x8+1x4+1x2+1x1
=> 64+0+0+8+4+2+1
=> 79
Answer: -79