ITPEC FE Morning October 2023 Question 4

Binary Fraction Addition — add two binary fractions and convert to decimal.

Add 1.0101 + 1.0111 in binary:

• •Align and add column by column (right to left):
• •1+1 = 10 → write 0, carry 1
• •0+1+1 = 10 → write 0, carry 1
• •1+1+1 = 11 → write 1, carry 1
• •0+0+1 = 1 → write 1
• •1+1 = 10 → write 0, carry 1
• •Result: 10.1100

Convert 10.1100 to decimal:

• •Integer part: 10 = 2
• •Fractional part: .1100 = 1×2⁻¹ + 1×2⁻² + 0 + 0 = 0.5 + 0.25 = 0.75
• •Total = 2 + 0.75 = 2.75

Why not others:
- (a) 2.5 — misses fractional carry bits
- (c) 2.875 — incorrect carry propagation
- (d) 2.9375 — adds fractional parts without carrying

Key rule: Binary fraction addition follows the same carry rules as integer addition; convert each fractional bit as 2⁻¹, 2⁻², 2⁻³, ...

AI-generated — may contain errors