Test by Bikram | Computer Organization and Architecture | Test 2 | Question: 6

Question

 We want to represent the decimal number $“1000”$ in one’s complement, two’s complement and sign magnitude representations, respectively, which option correctly represent it?

• A. $-7,+8,-0$
• B. $-7,-8,0$
• C. $-7,-8,-0$
• D. $+7,+8,-0$

Answer 1

1000 in binary 11 1110 1000

1. For 1's complement , 00 0001 0111 = 10111 = -(4+2+1) = -7  [ bit by bit complement only]
2. For 2's complement , 1000 in binary 11 1110 1000   

           complement is   00 0001 0111 

             add 1              00 0001 1000, so 2's complement is 11000 = -8  [ bit by bit complement +1 ]

For sign magnitude representation,  1000 , left most bit or MSB is 1  so sign is  -ve , rest three bits are 0 so 1000 in sign magnitude representation is -0

so 1000 in 1's, 2's complement and sign magnitude is -7, -8, -0 

which is option C .

Comments

@ arjun sir you have written directly sign magnitude using 1000 as binary but its in decimal isnt it wrong...?

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Decimal Number(1000)₁₀=(1111101000)₂ Binary Number

So in Sign Magnitude, it should represent  1 (sign bit) 111101000(Data bit) =-488

Please Check It!

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@Bikram Sir,

Since The Number 1000 is positive in decimal then its 1’s and 2’s complements remain the same ie:(1111101000)

please sir tell me where I’m doing a mistake??

Answer 2

Answer should be

-7 -8 -0