GateAI
Number Representation and Arithmetic

GATE CSE 2019 · Q4

MCQ1 markEasy

Time

In 16-bit 2's complement representation, the decimal number −28-28 is:

Select one answerSingle correct

Pick an option to check

Solution

Step-by-step verified solution

Official answer: C) 1111 1111 1110 0100

Number Representation and Arithmetic

To represent −28-28 in 16-bit 2's complement:

  1. Find the 16-bit binary representation of +28+28:

    +28=(0000 0000 0001 1100)2+28 = (0000\ 0000\ 0001\ 1100)_2
  2. Compute its 1's complement (invert all bits):

    1111 1111 1110 00111111\ 1111\ 1110\ 0011
  3. Add 11 to get the 2's complement:

    1111 1111 1110 0011+1=1111 1111 1110 01001111\ 1111\ 1110\ 0011 + 1 = 1111\ 1111\ 1110\ 0100

This matches option (C).

Try the question first, then check your work.

Think the official key or this write-up is wrong?

Report error or challenge

Examiner trap

The misconception this question tests

This Number Representation and Arithmetic previous year question is Q4 of the GATE CSE 2019 paper. Find more GATE CSE PYQs on Number Representation and Arithmetic in Digital Logic, or browse all GATE CSE PYQs.

Free diagnostic

Where do you stand for GATE?

Take the 20-minute diagnostic: the 3 topics that cost you the most marks, and a rank range. Or sit 5 related Number Representation and Arithmetic PYQs now with no account.

One GATE CSE PYQ every morning

An official question by email at 7 AM IST, with a link to its verified solution. Unsubscribe in one click.

Number Representation and Arithmetic in GATE CSE

Number Representation and Arithmetic has 33 GATE CSE PYQs across 20 papers from 2012 to 2026. 13 of them are 1-mark MCQs like this one, and GATE CSE 2019 has 2.

How GATE tests Number Representation and Arithmetic

More from GATE CSE 2019

Share this solution

A plain-text card for WhatsApp or Telegram study groups.

GateAI solution cardGATE CSE 2019 · Q4 · MCQ

In 16-bit 2's complement representation, the decimal number -28 is:

Topic-wise GATE CS PYQs with verified steps

Independent practice explanation verified by the GateAI team. GATE is conducted by the IITs; question text follows the official paper.