The decimal number (127.25)₁0},when converted to binary number, takes the form [NDA I 2015]

Correct Answer is : (1111111.01)2(1111111.01)₂(1111111.01)2

Correct Answer is : (1111111.01)2(1111111.01)₂(1111111.01)2

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NDA Math Binary Numbers

Question : 8 of 13

Marks: +1, -0

(127.25)_{10}

Solution:

Consider the whole number 127. Hence it can be converted into Binary into following steps

127

i)127=2(63)+1\rightarrow1

ii)63=2(31)+1\rightarrow1

iii)31=2(15)+1\rightarrow1

iv)15=2(7)+1\rightarrow1

v)7=2(3)+1\rightarrow1

vi)3=2(1)+1\rightarrow1

vii)1=2(0)+1\rightarrow1

(127)_{10}\rightarrow(1111111)_2

Hence, the binary of 127 is seven times 1 or (1111111).

Now for the binary of the number after the point, we get

0.25\times 2=0.5\rightarrow0

0.5\times 2=1.0\rightarrow0

\therefore (0.25)_{10}=(.01)_2

\therefore (127.25)-10=(1111111.01)_2

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