ITPEC FE Morning April 2019 Question 1

Shift 2 bits to the left, then add the original value — 5x = 4x + x, and a 2-bit left shift multiplies by 4.

In two's complement, a left shift by k bits multiplies by 2^k and an arithmetic right shift by k bits divides by 2^k, keeping the sign.

• •Write 5 as a power of two plus a small term: 5 = 4 + 1 = 2² + 1
• •Shift x 2 bits to the left: 4x
• •Add x: 4x + x = 5x

Answer (b)

Why not others:

• •(a) — a 1-bit shift is only ×2, so the result is 2x + x = 3x
• •(c) — a right shift divides instead of multiplying: x ÷ 2 − x = −x ÷ 2
• •(d) — likewise x ÷ 4 − x = −3x ÷ 4, a fraction of x with the wrong sign

Key rule: To multiply by a constant with shifts, write it as a sum or difference of powers of two, such as 5 = 2² + 1 or 7 = 2³ − 1, and use left shifts; right shifts divide.

Basic Theory · AI-written, may contain errors