ITPEC IP April 2021 Question 3

Topic: Basic TheoryAlso asked in October 2018

Which of the following is obtained by multiplying the binary value 10110 by three (3)?

Explanation

1000010 — multiplying by 3 is the same as adding the number shifted left once (×2) to itself (×1).

  • •3x = 2x + x: 10110 shifted left one place is 101100
  • •101100 + 10110 = 1000010, with carries
  • •Check in decimal: 10110 is 16 + 4 + 2 = 22, and 22 × 3 = 66 = 64 + 2, which is 1000010

Answer (c)

Why not others:

  • •(a) 111010 — adds 101100 and 10110 digit by digit but drops every carry (an XOR); it is 58
  • •(b) 111110 — writes a 1 wherever either number has a 1 (an OR), again ignoring carries; it is 62
  • •(d) 10110000 — shifts left three places, which multiplies by 23 = 8, not by 3; it is 176

Key rule: A left shift by n multiplies by 2n; to multiply by a number that is not a power of 2, add shifted copies (3x = 2x + x) and carry as in decimal addition.

Basic Theory · AI-written, may contain errors

Practice this exam

This question comes from an official ITPEC past paper. ITPEC Practice is an independent study tool and is not affiliated with ITPEC. See the official IP past-paper collection or Report an issue.