Question

1. Complete the following table using 8-bit representation ((show your work to get credit)

Decimal	Signed Magnitude	One’s Complement	Two’s Complement
30
-47
0

Answer 1

Question 1:
Number is 30
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.
30 /  2  result 15 remainder  0
15 /  2  result 7  remainder  1
7  /  2  result 3  remainder  1
3  /  2  result 1  remainder  1
1  /  2  result 0  remainder   1
Read the remainders from bottom to top.
( 30 )10 = ( 11110 )2
prepend zeros to make it 8-bit
( 30 )10 = ( 00011110 )2

As it is positive number all Signed Magnitude, One’s Complement, Two’s Complement are same as 00011110

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Question 2:
Number is -47
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.
47 /  2  result 23 remainder  1
23 /  2  result 11 remainder  1
11 /  2  result 5  remainder  1
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.
( 47 )10 = ( 101111 )2
prepend zeros to make it 8-bit
( 47 )10 = ( 00101111 )2

-47 in Signed Magnitude = Replace most significant bit to 1 = 10101111
-47 in One’s Complement = Invert bits in binary = 11010000
-47 in Two’s Complement = Ones complement + 1 = 11010001

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Question 3:
Number is 0
0 in 8-bit binary is 00000000
All Signed Magnitude, One’s Complement, Two’s Complement are same as 00000000

Decimal	Signed Magnitude	One’s Complement	Two’s Complement
30	00011110	00011110	00011110
-47	10101111	11010000	1101000
0	00000000	00000000	00000000