Assuming integers are represented as 32-bit words and negative numbers are represented using the 2's complimentary...

Assuming integers are represented as 32-bit words and negative numbers are represented using the 2's complimentary method convert the following decimal numbers to hexadecimal numbers (show your work). a. -1314, b. 2020

Expert Solution

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
using this table for converting binary to hexadecimal

a)
This is negative. so, follow these steps to convert this into a 2's complement binary
Step 1:
Step 1. Divide 1314 successively by 2 until the quotient is 0
1314/2 = 657, remainder is 0
657/2 = 328, remainder is 1
328/2 = 164, remainder is 0
164/2 = 82, remainder is 0
82/2 = 41, remainder is 0
41/2 = 20, remainder is 1
20/2 = 10, remainder is 0
10/2 = 5, remainder is 0
5/2 = 2, remainder is 1
2/2 = 1, remainder is 0
1/2 = 0, remainder is 1
Read remainders from the bottom to top as 10100100010

So, 1314 in normal binary is 00000000000000000000010100100010
Step 2: flip all the bits
   00000000000000000000010100100010 is flipped to 11111111111111111111101011011101
Step 3:. Add 1 to above result
11111111111111111111101011011101 + 1 = 11111111111111111111101011011110
so, -1314 in 2's complement binary is 11111111111111111111101011011110
11111111111111111111101011011110 in hexadecimal is 0xFFFFFADE

Answer: 0xFFFFFADE

b)
Since this is a positive number. we can directly convert this into binary
Step 1. Divide 2020 successively by 2 until the quotient is 0
2020/2 = 1010, remainder is 0
1010/2 = 505, remainder is 0
505/2 = 252, remainder is 1
252/2 = 126, remainder is 0
126/2 = 63, remainder is 0
63/2 = 31, remainder is 1
31/2 = 15, remainder is 1
15/2 = 7, remainder is 1
7/2 = 3, remainder is 1
3/2 = 1, remainder is 1
1/2 = 0, remainder is 1
Read remainders from the bottom to top as 11111100100

so, 2020 in 2's complement binary is 00000000000000000000011111100100
00000000000000000000011111100100 in hexadecimal is 0x000007E4

Answer: 0x000007E4

venereology answered 10 months ago

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