Question

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1. What is the Binary representation of this Decimal? (signed) 115

2. What is the Hexadecimal representation of this Decimal? (signed) 220

3. Convert the following from Signed Decimal to Hexadecimal: (signed) -24

Answer 1

1)
115
Since this is a positive number. we can directly convert this into binary
Divide 115 successively by 2 until the quotient is 0
   > 115/2 = 57, remainder is 1
   > 57/2 = 28, remainder is 1
   > 28/2 = 14, remainder is 0
   > 14/2 = 7, remainder is 0
   > 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 1110011
So, 115 of decimal is 1110011 in binary
so, 115 in 2's complement binary is 01110011
Answer: 01110011

2)
Divide 220 successively by 16 until the quotient is 0
220/16 = 13, remainder is 12
13/16 = 0, remainder is 13
Read remainders from the bottom to top as DC
Answer: 0xDC

3)
-24
This is negative. so, follow these steps to convert this into a 2's complement binary
Step 1:
Divide 24 successively by 2 until the quotient is 0
   > 24/2 = 12, remainder is 0
   > 12/2 = 6, remainder is 0
   > 6/2 = 3, remainder is 0
   > 3/2 = 1, remainder is 1
   > 1/2 = 0, remainder is 1
Read remainders from the bottom to top as 11000
So, 24 of decimal is 11000 in binary
So, 24 in normal binary is 00011000
Step 2: flip all the bits. Flip all 0's to 1 and all 1's to 0.
   00011000 is flipped to 11100111
Step 3:. Add 1 to above result
11100111 + 1 = 11101000
so, -24 in 2's complement binary is 11101000

Now convert 11101000 to hexadecimal
Converting 11101000 to hexadecimal
1110 => E
1000 => 8
So, in hexadecimal 11101000 is 0xE8
Answer: 0xE8