NIMCET 1s Complement 2s Complement Previous Year Question Paper and Solution with PDF

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NIMCET Previous Year Questions (PYQs)

NIMCET 1s Complement 2s Complement PYQ

Qus : 1 NIMCET PYQ

Consider the following statements about the range of numbers in a $9$-bit $1$'s complement and $2$'s complement system.

I. In $9$-bit $1$'s complement, the range is $-255$ to $+255$, and there exist two representations of zero.

II. In $9$-bit $2$'s complement, the range is $-256$ to $+255$, and both $1$'s complement and $2$'s complement can represent exactly $512$ unique values.

III. The maximum positive number representable is $+255$ in both $1$'s complement and $2$'s complement $9$-bit systems.

Identify the CORRECT option.

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NIMCET Previous Year PYQ NIMCET NIMCET 2026 PYQ

Solution

For $9$-bit $1$'s complement, the range is

$-(2^{8}-1)$ to $+(2^{8}-1)$

$=-255$ to $+255$

Also, in $1$'s complement, there are two representations of zero: positive zero and negative zero.

So, statement I is correct.

For $9$-bit $2$'s complement, the range is

$-2^8$ to $2^8-1$

$=-256$ to $+255$

But $1$'s complement does not represent exactly $512$ unique values because zero has two representations.

So, statement II is incorrect.

The maximum positive number in both systems is

$+255$

So, statement III is correct.

Therefore, statements I and III only are correct.

Qus : 2 NIMCET PYQ

Consider a 9-bit representation. Which of the following correctly gives the smallest number that can be represented in:

(i) 1's complement,

(ii) 2's complement

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NIMCET Previous Year PYQ NIMCET NIMCET 2025 PYQ

Solution

For an n-bit system:

1’s complement range: $-(2^{n-1}-1)$ to $+(2^{n-1}-1)$ ⇒ smallest $=-(2^{8}-1)={-255}$.
2’s complement range: $-2^{n-1}$ to $+(2^{n-1}-1)$ ⇒ smallest $=-2^{8}={-256}$.

(9-bit means sign + 8 magnitude bits.)

Qus : 3 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 PYQ NIMCET NIMCET 2017 PYQ

Solution

Qus : 4 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 Previous Year PYQ NIMCET NIMCET 2017 PYQ

Solution

✅ Given Information:

An 8-bit number in 2's complement form can represent values from $-2^{n-1}$ to $2^{n-1} - 1$.

✅ Step 1: Calculate the smallest integer:

Smallest value = $-2^{8-1} = -2^7 = -128$

✅ Final Answer:

The smallest integer that can be represented by an 8-bit number in 2's complement form is: -128

Qus : 5 NIMCET PYQ

What is the 2's complement of 0011 0101 1001 1100?

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NIMCET Previous Year PYQ NIMCET NIMCET 2014 PYQ

Solution

Qus : 6 NIMCET PYQ

What is the 8 bit 2's complement representation of the negative integer-93?

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NIMCET Previous Year PYQ NIMCET NIMCET 2014 PYQ

Solution

Qus : 7 NIMCET PYQ

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

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NIMCET Previous Year PYQ NIMCET 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

Qus : 8 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 Previous Year PYQ NIMCET NIMCET 2019 PYQ

Solution

Qus : 9 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 Previous Year PYQ NIMCET NIMCET 2019 PYQ

Solution

Qus : 10 NIMCET PYQ

A computer with a 32 bit word size uses 2’s complement to represent numbers. The range of integers that can be represented by this computer is:

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NIMCET Previous Year PYQ NIMCET NIMCET 2009 PYQ

Solution

In $n$-bit 2’s complement, range is $-2^{n-1}$ to $2^{n-1}-1$.

Qus : 11 NIMCET PYQ

When two binary numbers are added, then an overflow will never occur if

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NIMCET Previous Year PYQ NIMCET NIMCET 2011 PYQ

Solution

Overflow never occurs when carry into sign bit = carry out of sign bit.

Qus : 12 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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NIMCET Previous Year PYQ NIMCET NIMCET 2024 PYQ

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

Qus : 13 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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NIMCET Previous Year PYQ NIMCET NIMCET 2024 PYQ

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

Qus : 14 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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NIMCET Previous Year PYQ NIMCET NIMCET 2024 PYQ

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.

Qus : 15 NIMCET PYQ

Let x = 11111010 and y = 00001010 be two 8-bit 2’s complement numbers. Their product in 2’s complement notation is

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NIMCET Previous Year PYQ NIMCET NIMCET 2012 PYQ

Solution

Qus : 16 NIMCET PYQ

The range of numbers that can be stored in 8 bits, if negative numbers are stored in 2’s complement form is

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NIMCET Previous Year PYQ NIMCET NIMCET 2012 PYQ

Solution

Qus : 17 NIMCET PYQ

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

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NIMCET Previous Year PYQ NIMCET NIMCET 2022 PYQ

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 $32767$

Qus : 18 NIMCET PYQ

The 2's complement representation of the number (–100)₁₀ in an 8 bit computer is

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NIMCET Previous Year PYQ NIMCET NIMCET 2016 PYQ

Solution

Qus : 19 NIMCET PYQ

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

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NIMCET Previous Year PYQ NIMCET NIMCET 2016 PYQ

Solution

Qus : 20 NIMCET PYQ

The range of n-bit signed magnitude representation is

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NIMCET Previous Year PYQ NIMCET NIMCET 2016 PYQ

Solution

For an $n$-bit Signed Magnitude Representation:
The leftmost bit (MSB) is the sign bit:
$0 \rightarrow$ Positive
$1 \rightarrow$ Negative
Remaining $(n-1)$ bits represent the magnitude
Maximum positive value:
Sign bit $= 0$, remaining $(n-1)$ bits all $1$s
$\Rightarrow +(2^{n-1} - 1)$
Maximum negative value:
Sign bit $= 1$, remaining $(n-1)$ bits all $1$s
$\Rightarrow -(2^{n-1} - 1)$
Note: $+0$ and $-0$ both exist in signed magnitude representation
$\therefore$ Range of $n$-bit Signed Magnitude Representation is:
$\therefore \boxed{-(2^{n-1}-1) \leq x \leq +(2^{n-1}-1)}$

Qus : 21 NIMCET PYQ

An embedded computer uses $8$-bit $2$'s complement representation for signed integers. What is the minimum negative integer value which can be represented in this computer?

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NIMCET Previous Year PYQ NIMCET NIMCET 2026 PYQ

Solution

In $n$-bit $2$'s complement representation, the range of signed integers is:

$-2^{n-1}$ to $2^{n-1}-1$

Here,

$n=8$

So, range is:

$-2^{7}$ to $2^{7}-1$

$=-128$ to $127$

Therefore, the minimum negative integer value is $-128$.

Qus : 22 NIMCET PYQ

The addition of 4 bit, 2’s complement binary numbers 1101 and 0100 results in

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NIMCET Previous Year PYQ NIMCET NIMCET 2008 PYQ

Solution

1101 is a 4-bit 2’s complement number.

Its MSB is 1, so it is negative.

1101 = −3

0100 = +4

Adding:

1101

+0100

=10001

Taking only 4 bits → 0001

Qus : 23 NIMCET PYQ

Let A = 11111010 and B = 00001010 be two 8 bit 2’s complement numbers. Their product in 2’s complement is

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NIMCET Previous Year PYQ NIMCET NIMCET 2008 PYQ

Solution

A = 11111010 → −6

B = 00001010 → +10

Product = −60

+60 in binary = 00111100

2’s complement of 00111100 = 11000100

Qus : 24 NIMCET PYQ

Which one of the following is decimal equivalent of $8$-bit two's complement number $11010011$?

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NIMCET Previous Year PYQ NIMCET NIMCET 2026 PYQ

Solution

Given $8$-bit two's complement number is:

$11010011$

Since the leftmost bit is $1$, the number is negative.

To find its magnitude, take two's complement.

First, invert all bits:

$11010011\to 00101100$

Now add $1$:

$00101100+1=00101101$

Now convert $00101101$ to decimal:

$00101101=32+8+4+1$

$=45$

Since the original number was negative, the decimal equivalent is:

$-45$

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NIMCET Previous Year Questions (PYQs)

NIMCET 1s Complement 2s Complement PYQ

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Solution

✅ Given Information:

✅ Step 1: Calculate the smallest integer:

✅ Final Answer:

Solution

Solution

Solution

Maximum & Minimum in 16-bit 2's Complement

Solution

Solution

Solution

Solution

Solution

2's Complement Addition (4-bit)

Solution

2's Complement Addition (8-bit)

Solution

Binary to Decimal: 2's Complement Conversion

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