ITPEC FE Subject A April 2026 Question 2

668.25 — multiply each octal digit by its power of 8, with negative powers after the point.

• •Integer part: 1 × 8³ + 2 × 8² + 3 × 8 + 4 = 512 + 128 + 24 + 4 = 668
• •Fraction part: 2 × 8⁻¹ = 2 ÷ 8 = 0.25
• •Total: 668 + 0.25 = 668.25

Answer (b)

Why not others:

• •(d) 5346.0 — ignores the octal point and converts 12342 as an integer, which is the true value times 8: 668.25 × 8 = 5346
• •(a) 27.0 — below 1000₈ = 512, yet the number has four octal digits before the point
• •(c) 1542.5 — above 2000₈ = 1,024, yet the leading digit is only 1

Key rule: In base r, digits left of the point carry r⁰, r¹, r² … and digits right of it carry r⁻¹, r⁻² …; bounding the value by the leading digit catches wrong options fast.

Basic Theory · AI-written, may contain errors