Question

Part 2: Signed values: Convert each as indicated.

7. Decimal to Hexadecimal (1 byte, signed magnitude)

     a. -18

     b. -41

Answer 1

a. -18
Decimal to binary:
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Write down the decimal number and continually divide by 2 to give a result and a remainder. The remainder is either a 1 or a 0.
18 /  2  result 9  remainder  0
9  /  2  result 4  remainder  1
4  /  2  result 2  remainder  0
2  /  2  result 1  remainder  0
1  /  2  result 0  remainder  1
Read the remainders from bottom to top.
( 18 )10 = ( 10010 )2
Prepend zeros ro make it 8 bit.
( 18 )10 = ( 00010010 )2

Ones complement = Inverts bits in binary = 11101101
Twos complement = Ones complement + 1 = 11101101 + 1 = 11101110

Binary to hexa decimal:
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Convert each 4 bits to its hexa decimal.
1110 in hexa decimal is E
So, 11101110 in hexa decimal = EE

Answer: (EE)16

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b. -41
Decimal to binary:
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Write down the decimal number and continually divide by 2 to give a result and a remainder. The remainder is either a 1 or a 0.
41 /  2  result 20 remainder  1
20 /  2  result 10 remainder  0
10 /  2  result 5  remainder  0
5  /  2  result 2  remainder  1
2  /  2  result 1  remainder  0
1  /  2  result 0  remainder  1
Read the remainders from bottom to top.
( 41 )10 = ( 101001 )2
Prepend zeros ro make it 8 bit.
( 41 )10 = ( 00101001 )2

Ones complement = Inverts bits in binary = 11010110
Twos complement = Ones complement + 1 = 11010110 + 1 = 11010111

Binary to hexa decimal:
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Convert each 4 bits to its hexa decimal.
1101 in hexa decimal is D
0111 in hexa decimal is 7
So, 11010111 in hexa decimal = D7

Answer: (D7)16