GATE Computer Science (CS) 2018 Shift 1 Solved Paper

Question : 49 of 65

Marks: +1, -0

Consider the unsigned 8-bit fixed point binary number representation below :

b_{1} b_{6} b_{5} b_{4} b_{3} ⋅ b_{2} b_{1} b_{0}

Where the position of the binary point is between

b_{3}

and

b_{2} .

Assume

b_{7}

is the most significant bit. Some of the decimal numbers listed below cannot be represented exactly in the abo' representation: i. 31.500 ii. 0.875 iii. 12.100 iv. 3.001
Which one of the following statements is true?

None of (i), (ii), (iii), (iv) can be exactly represented.
Only (ii) cannot be exactly represented.
Only (iii) and (iv) cannot be exactly represented.
Only (i) and (ii) cannot be exactly represented.

Validate

Solution:

Binary code:

(b, b_{6} b_{5} b_{4} b_{3} ⋅ b_{2} b_{1} b_{0})_{2}

(31.5)_{10}=(11111.1)_{2}

(0.875)_{10}=(0.111)_{2}

(12.100)_{10}=(01100.000110 . . . . . .)_{2}

Only 3 bits of fraction space available. So can't be stored.

(3.001)_{10}=(00011.000000 . . . . . . . . .)_{2}

It is also not accurate storage.

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