ITPEC FE Subject A April 2025 Question 2

10111.011 — convert the integer part and the fraction separately, then join them.

• •Integer part: 23 = 16 + 4 + 2 + 1, so 10111
• •Fraction: 0.375 = 0.25 + 0.125 = 2^-2 + 2^-3, so .011

The same fraction by repeated doubling: 0.375 × 2 = 0.75 gives 0, 0.75 × 2 = 1.5 gives 1, 0.5 × 2 = 1.0 gives 1, read top to bottom as .011.

Answer (a)

Why not others:

• •(b) 10111.110 — .110 is 0.5 + 0.25 = 0.75: the fraction digits are read in reverse, bottom to top
• •(c) 11101.011 — 11101 is 29: the integer remainders are read in reverse, first to last
• •(d) 11101.110 — both parts reversed, 29.75

Key rule: For the integer part, divide by 2 and read the remainders from last to first; for the fraction, multiply by 2 and read the integer digits from first to last.

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