# Is this the right way to convert a negative floating point number in binary using two's complement method?

I'm a cs student and i've just started learning about binary arithmetic.I have to do this homework assignement to get prepared for exams..I'm having some trouble figuring out how to convert a negative floating point number in binary system....I was thiking about IEEE-754 representation but i must use only two's complement method...other than that i'm not really sure if my calculations are right ...I'm really confused.

So the exercise is:

1.Convert a=-9, b=+3.75, c= -1.25, d=+10.2 in binary using two's complement representation.For integer part you must use the minimum number of bits and for the fractional part only 4 bits.

2.Convert the above numbers in signed magnitude representation (in binary)

3.Calculate a-a , b+c , c+a using two's complement of question (1)

my solution:

1.9 as unsigned int in binary: 1001 so +9 is : 01001

-9 is : inversion of bits and then add 1 so : 01001 --> 10110+1-->10111

so a=10111

+3.75: 3 is 11 so +3: 0011 and 0.75: 0.11

together--> 0011.11 is this right? I think it should be 11.11 cause we want the minimum bits

b=0011.11

-1.25 : 1 is 1 in binary so +1: 0001 and 0.25 is : 0.01

together --> 0001.01

(Again i think it should be 01.01 or 1.01 )

then i invert the bits so 0001.01 --> 1110.10+0.01--> 1110.11

c=1110.11

Is this how we do it?

+10.2 : 10 is 1010 in binary so +10: 01010 and 0.2 is : 0.0011

together--> 01010.0011

d=01010.0011

2.Signed magnitude representation

-9 : 10110

+3.75 its the same : 0011.11

-1.25 : ????

+10.2 its the same : 1010.0011

3.a-a

a=-9 which means -a=9 so i have to do -9+9 and in binary:

10111+01001=100000...we discard 1 so result is 00000 which is 0 in decimal

b+c

(I added 4 bits after point cus fractional part must have 4 bits as it says)

0011.1100+1110.1100=10010.1000 we discard 1 so result is 0010.1000 and in decimal 2.5

c+a

01110.1100+10111.0000=100101.1100 we discard 1 so result is 00101.1100 but in decimal 00101 isn't -10 but 5 . I can't detect my mistake

I don't know if any of the above is right,so please correct me.Any help would be much appreciated!

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• 01110.1100+10111.0000=100101.1100 -- I can't follow the Q's and A's, but this looks like 14.75-9=5.75. No mistake? – dcromley Jun 12 '18 at 1:07