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NIMCET Previous Year Questions (PYQs)

NIMCET 1s Complement 2s Complement PYQ

NIMCET PYQ
Which of the following is the representation of decimal number (- 147) in 2's compliment notation on a 12-bit machine?





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NIMCET Previous Year PYQNIMCET NIMCET 2017 PYQ

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NIMCET PYQ
The smallest integer that can be represented by an 8 bit number in 2's complement form is





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NIMCET PYQ
The maximum and minimum value represented in signed 16-bit 2s compliment representation are





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NIMCET Previous Year PYQNIMCET NIMCET 2023 PYQ

Solution

 Maximum & Minimum in 16-bit 2's Complement

 Total Bits: 16

Format: 1 sign bit + 15 magnitude bits

  • Maximum (positive): 0111 1111 1111 1111(2) = +32,767
  • Minimum (negative): 1000 0000 0000 0000(2) = −32,768

✅ Final Answer:
Minimum = −32,768
Maximum = +32,767

NIMCET PYQ
If N is a 16-bit signed integer, then 2's complement representation of N is (F87B)16. The 2's complement representation of 8*N is





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NIMCET PYQ
In an 8 bit representation of computer system the decimal number 47 has to be subtracted from 38 and the result in binary 2's complement is _________






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NIMCET PYQ
Consider the following 4- bit binary numbers represented in the 2’s complement form : 1101 and 0100 What would be the result when we add them?





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Solution

2's Complement Addition (4-bit)

Given: 1101 and 0100 (in 2’s complement)

Step-by-step:

  • 1101 = −3 (in decimal)
  • 0100 = +4 (in decimal)
  • Sum = −3 + 4 = +1
  • +1 in 4-bit 2’s complement = 0001

✅ Final Answer: 0001

NIMCET PYQ
Given that numbers A and B are two 8 bit 2’s complement numbers with A = 11111111, B = 11111111. Then sum A + B is _________





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Solution

2's Complement Addition (8-bit)

Given:

  • A = 11111111 → (−1)
  • B = 11111111 → (−1)

Sum: −1 + (−1) = −2

Convert −2 to 8-bit 2's complement:

  • +2 = 00000010
  • Invert = 11111101
  • Add 1 = 11111110

✅ Final Answer: 11111110

NIMCET PYQ
Let the given number 11001, 1001 and 111001 be correspond to the 2’s complement representation. Then with which one of the following decimal number, the given numbers match





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Solution

Binary to Decimal: 2's Complement Conversion

Given binary numbers:

  • 11001 (5-bit)
  • 1001 (4-bit)
  • 111001 (6-bit)

Step-by-step (2's complement):

  • Each starts with 1 → negative number
  • Convert by inverting and adding 1
  • All result in binary 0111 → decimal 7
  • So final value = −7

✅ Final Answer: Each binary number corresponds to the decimal number −7.

NIMCET PYQ
The maximum and minimum value represented in signed 16 bit 2's complement representations are





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Solution

Range of 2's complement $-2^{n-1}$ to $2^{n-1}+1$

Range for 16 bits = $-2^{16-1}$ to $2^{16-1}+1$

Range for 16 bits = $-2^{15}$ to $2^{25}+1$

Range for 16 bits = $-32768$ to $32767$
NIMCET PYQ
The 2's complement representation of the number (–100)10 in an 8 bit computer is





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NIMCET PYQ
Subtract (1010)2 from (1101)2 using first complement





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NIMCET PYQ
The range of n-bit signed magnitude representation is





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