ITPEC FE Morning April 2018 Question 1

Bit Shift and Addition — what happens when you left-shift a binary value and then add the original.

Left-shifting a binary number by n bits multiplies it by 2ⁿ.

1. Start with register = x
2. Left shift by 2 bits → register = x × 2² = 4x
3. Add x → register = 4x + x = 5x

The register now holds 5x, so it is 5 times larger than x.

Why not others:
- (a) 3 — would require a 1-bit shift + add (2x + x)
- (b) 4 — would be just the shift without the addition (4x)
- (d) 6 — would require a 1-bit shift then add, then shift again, or some other combo

Key rule: Left shift by n bits = multiply by 2ⁿ. Then just do the arithmetic with any additions.

AI-generated — may contain errors