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Consider the unsigned 8-bit fixed-point binary number representation below, b7 b6 b5 b4 b3 . b2 b1 b0 where the position of the binary point is between b3 and b2. Assume b7 is the most significant bit. Some of the decimal numbers listed below cannot be represented exactly in the above representation: (i) 31.500 (ii) 0.875 (iii) 12.100 (iv) 3.001 Which one of the following statements is true?

Consider the unsigned 8-bit fixed-point binary number representation below, b7 b6 b5 b4 b3 . b2 b1 b0 where the position of the binary point is between b3 and b2. Assume b7 is the most significant bit. Some of the decimal numbers listed below cannot be represented exactly in the above representation: (i) 31.500 (ii) 0.875 (iii) 12.100 (iv) 3.001 Which one of the following statements is true? Correct Answer Only (iii) and (iv) cannot be exactly represented

The correct answer is option 3.

Concept:

Fixed-point number representation:

A real data type for a number is a fixed-point number representation. Data is translated into the binary form using fixed number representation, and then processed, stored, and utilized by the system.

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(i) 31.500:

(31.5)10 = (11111.100)2

 =24 + 23+22 + 21 + 20 + 2-1 = 16 + 8 + 4 + 2 + 1 + 0.5 = (31.05)10

(ii) 0.875:

(0.875)10 = (00000.111)2

=2-1 + 2-2+ 2-3 = 0.50 + 0.25 + 0.125 = (0.875)10

(iii) 12.100:

(12.100)10=(1100.00011)2 we can not represent exactly in the above representation.

(iv) 3.001:

(3.001)10=(11.0000000001000)2 we can not represent exactly in the above representation.

Hence the correct answer is Only (iii) and (iv) cannot be exactly represented.

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