ITPEC FE Morning October 2020 Question 1

Binary fraction by division — convert 7 / 32 to binary.

Since 32 = 2⁵, dividing by 32 means shifting the binary point 5 places left:

• •7 in binary = 111
• •Shift right by 5 → 0.00111

Result: 0.00111

Why not others:
- (a) 0.001011 — equals 11/64 ≈ 0.171875, not 7/32
- (b) 0.001101 — equals 13/64 ≈ 0.203125, not 7/32
- (d) 0.0111 — equals 7/16 (only 4-position shift instead of 5)

Key rule: Dividing by 2ⁿ = shifting the binary point n positions to the left.

AI-generated — may contain errors