ITPEC FE Morning October 2023 Question 2
Source exam: ITPEC FE Morning October 2023Topic: Basic Theory & Math
ITPEC FE Morning October 2023 — Question 2 of 80
Bit Shifting for Multiplication — compute 7 × n using shift and add/subtract.
Key idea: decompose the multiplier into powers of 2, then use shifts.
7 = 8 - 1 = 2³ - 1, so:7n = (n << 3) - n
- •(a)
(n << 2) + n=4n + n=5n - •(b)
(n << 2) - n=4n - n=3n - •(c)
(n << 3) + n=8n + n=9n - •(d)
(n << 3) - n=8n - n=7n✓
Key rule: Left shift by k bits = multiply by 2^k. Decompose any multiplier into sums/differences of powers of 2.
Common patterns:
- 3n = (n << 1) + n
- 5n = (n << 2) + n
- 7n = (n << 3) - n
- 9n = (n << 3) + n
AI-generated — may contain errors
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