ITPEC FE Subject A April 2024 Question 1

291.25 — expand each hex digit by its power of 16, using negative powers after the point.

• •Integer part: 1 × 16² + 2 × 16¹ + 3 × 16⁰ = 256 + 32 + 3 = 291
• •Fraction: 4 × 16^-1 = 4 ÷ 16 = 0.25
• •Total: 291 + 0.25 = 291.25

Answer (c)

Why not others:

• •(a) 83.25 — reads the integer part as octal, 1 × 8² + 2 × 8 + 3 = 83, but keeps the hex fraction
• •(b) 83.5 — reads the whole number as octal: 83 plus 4 ÷ 8 = 0.5
• •(d) 291.5 — the integer part is right, but the fraction digit is divided by 8 instead of 16

Key rule: Each digit after the radix point is worth one more negative power of the base: in hex the first is divided by 16, the second by 256.

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