FLoating Point Arithmetic

Question

what is  Nega Binary representation of (41)_{10 ?}

I just google first about negaBinary (-2 ) , The procedure says divide number by -2 , to get positive remainder and then read from bottom to top 

But my answer doesnt match with the answer given in book

(41) = (-2)*(-20) + 1(LSB)

-20 = (-2)*(10) + 0 

(10)= (-2)*(5) + 0

(5) = (-2)*(-2) +1

(-2)= (-2)*(1) +0

1 = (-2)*(0) + 1 (MSB)

So answer what i get is 101001

But they give answer = 1111101

Can you please explain and correct me ?

 

Comments

The procedure you had done is for converting decimal to binary - not to negabinary. Negabinary is given in the wiki link but is it required for GATE? I'm hearing for first time :)

http://en.wikipedia.org/wiki/Negative_base

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oops ! now ?

Answer 1

The base  expansion of a number can be found by repeated division by , recording the non-negative remainders of , and concatenating those remainders, starting with the last. Note that if , remainder , then . 

for 41 it should be like this,

41/-2 = -20, remainder 1

-20/-2 = 10, remainder 0

10/-2 = -5, remainder 0

-5/-2 = 3, remainder 1

3/-2 = -1, remainder 1

-1/-2 = 1, remainder 1

1/-2 = 0, remainder 1

so the nega binary of 41 is 1111001.

Wikipedia covers it in detail.