Question

Show the decimal integer 44 in 7-bit sign magnitude, one's complement, two's complement and excess-63 respectively in the given order, separated by comma.

Answer 1

Answer:
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0101100,0101100,0101100,1101011

44
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Since this is a positive number. we can directly convert this into binary
Divide 44 successively by 2 until the quotient is 0
   > 44/2 = 22, remainder is 0
   > 22/2 = 11, remainder is 0
   > 11/2 = 5, remainder is 1
   > 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 101100
So, 44 of decimal is 101100 in binary
Adding 1 zero(s) on left hand side of this number to make this of length 7
So, 44 in normal binary format is 0101100
====================================
||    1's complement: 0101100    ||
||    2's complement: 0101100    ||
||    sign-magnitude: 0101100    ||
====================================

for excess-63:
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add 63 to 44
63+44 = 107
107 in 7-bit binary is
Divide 107 successively by 2 until the quotient is 0
   > 107/2 = 53, remainder is 1
   > 53/2 = 26, remainder is 1
   > 26/2 = 13, remainder is 0
   > 13/2 = 6, remainder is 1
   > 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 1101011
So, 107 of decimal is 1101011 in binary