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8-bit 1's complement form of -77.25

a) 01001101.0100

b)01001101.0010

c)10110010.1011

d)10110010.1101

2 Answers

Best answer
2 votes
2 votes

For storing a negative decimal number in 1's complement representation, just find the binary representation of the decimal number and find the 1's complement by negating it.

Here, 77 in binary can be found out by: $2^7*0+2^6*1+2^5*0+2^4*0+2^3*1+2^2*1+2^1*0+2^0*1$ which is 01001101

For converting fraction .25 to binary, just multiply the fraction by 2 repeatedly, ignoring the whole number part each time as given below:

$0.25*2=0.5$

$0.5*2=1.0$  We stop, beacause the fractional part has reached 0.

Writing down the whole number parts, we get 01

Therefore, the binary of 77.25 is 01001101.01000... (Any number of trailing zeros doesn't matter)

For any decimal number x, negating its binary representation yields binary representation of -x in 1's complement representation.

Therefore, --77.25 is 10110010.1011 (Any number of trailing 1's doesn't matter)

Answer is (c).

edited by
1 votes
1 votes

Conecpt :- Suppose i want 1's and 2's complement representation of -5 then 

step1:-> write +5 as signed no.=0101

step2:->1's of(+5)=1010= 1's  complement representation of -5

step3:->2's of(+5)=1011=2's complement representation of -5

Similarly here i want 1's and 2's complement representation of -77.25 then 

step1:->write +77.25 as signed no.=0100 1101.0100 

step2:->1's of(+77.25)=1011 0010.1011= 1's  complement representation of -77.25 //Hence Option C is Ans

step3:->2's of(+77.25)=1011 0010.1100=2's complement representation of -77.25

http://stackoverflow.com/questions/15463491/how-to-represent-a-negative-number-with-a-fraction-in-2s-complement/39446894#39446894

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