Phrases Data Representation - Number System Previous Year Question Paper and Solution with PDF

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Phrases Data Representation - Number System PYQ

Qus : 1 Phrases PYQ

If we can generate a maximum of 4 Boolean functions using n Boolean variables, what will be minimum value of n?

NIMCET PREVIOUS YEAR QUESTION

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Phrases Computer PYQ Phrases Boolean algebra PYQ

Solution

Formula: Number of Boolean functions of $n$ variables is:

$ 2^{2^n} $

Condition: We are told the total functions must be ≤ 4:

\[ 2^{2^n} \leq 4 \]

✅ Try values of $n$:

$n = 0$: $2^{2^0} = 2^1 = 2$ ✅
$n = 1$: $2^{2^1} = 2^2 = 4$ ✅
$n = 2$: $2^{2^2} = 2^4 = 16$ ❌

Minimum $n$ for which number of Boolean functions ≤ 4 is:

\[ \boxed{1} \]

✅ Final Answer: $\boxed{1}$

Qus : 2 Phrases PYQ

The representation of a floating point binary number +1001.11 in 8 bit fraction and 6 bit exponent format is

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Phrases Previous Year PYQ Phrases NIMCET 2017 PYQ

Solution

✅ Given:

The floating-point binary number is $ +1001.11_2 $.

We need to convert it into an 8-bit fraction and a 6-bit exponent format.

✅ Step 1: Normalize the Binary Number

We start by normalizing the binary number into scientific notation of the form:

$ 1.xxxx \times 2^n $

Converting $ 1001.11_2 $ into scientific notation gives:

$ 1001.11_2 = 1.00111_2 \times 2^3 $

The exponent is $ 3 $ (because the binary point is shifted 3 places to the left).

✅ Step 2: Convert the Exponent to Binary

The exponent is $ 3 $ in decimal. To represent this in binary using 6 bits, we get:

$ \text{Exponent} = 000100_2 $

✅ Step 3: Convert the Fraction to 8 Bits

The fractional part of the normalized binary number is $ 00111 $. We need to extend it to 8 bits:

$ \text{Fraction} = 01001110_2 $

✅ Final Answer:

The floating-point binary number $ +1001.11_2 $ in 8-bit fraction and 6-bit exponent format is:

Exponent: $ 000100_2 $, Fraction: $ 01001110_2 $

Qus : 3 Phrases PYQ

Consider the equation (40)_x = (132)_y is some bases x and y. Then a possible set of value of x and y are

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Phrases Previous Year PYQ Phrases NIMCET 2017 PYQ

Solution

$\begin{array}{ll}{{{(40})}_x={{(132)}}_y} \\ {\Rightarrow4\times{x}^1}+0\times{x}^0=1\times{y}^2+3\times{y}^1+2\times{y}^0 \\ {\Rightarrow4x+0={y}^2+3y^{}+2} \\ {4x={y}^2+3y^{}+2}\end{array}$

Qus : 4 Phrases PYQ

How many bytes are there in a nibble?

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Phrases Previous Year PYQ Phrases NIMCET 2014 PYQ

Solution

Qus : 5 Phrases PYQ

Suppose we have a 10-bit computer that uses 10-bit int (2's complement representation). the number representation of - 35 is

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Phrases Previous Year PYQ Phrases NIMCET 2023 PYQ

Solution

10-bit 2's Complement Representation of –35

Format: 10-bit signed integer using 2's complement representation.

Step-by-Step:

First, convert 35 to 10-bit binary: 0000100011
Find 1's complement: 1111011100
Add 1 (to get 2's complement): 1111011101

✅ Final Answer: 1111011101

–35 in 10-bit 2's complement: 1111011101

Qus : 6 Phrases PYQ

What is a potential problem of 1’s complement representation of numbers?

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Phrases Previous Year PYQ Phrases NIMCET 2023 PYQ

Solution

Problem of 1’s Complement Representation

1. Two Zeros Exist
• Positive Zero: 0000
• Negative Zero: 1111
? This creates ambiguity, because logically both are zero but they have different bit patterns.

2. End-Around Carry Needed
When adding numbers, if a carry comes out of the MSB, it must be added back to the LSB.
(+5) = 0101 (-5) = 1010 (1’s complement of 0101) ---------------- Add: 1111 → End-around carry = 1 Final: 0000 (after adding carry)
? Result is zero, but note that two different zeros are possible.

3. Hardware Complexity
Extra logic is required so that +0 and -0 are treated the same, making design slower and costlier.

✅ Conclusion

That’s why modern systems use 2’s complement. It has only one zero and simplifies arithmetic operations.

Qus : 7 Phrases PYQ

In IEEE single precision floating point representation, exponent is represented in ______

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Phrases Previous Year PYQ Phrases NIMCET 2019 PYQ

Solution

IEEE 754 Single Precision Floating Point

Total Size: 32 bits

Sign bit: 1 bit
Exponent: 8 bits (biased, excess-127 notation)
Mantissa (Fraction): 23 bits

? Exponent Representation

The exponent is stored in 8-bit biased form with a bias of 127.
Stored exponent = Actual exponent + 127

Example:
Actual exponent = 3
Stored exponent = 3 + 127 = 130 = 10000010

✅ Conclusion

In IEEE single precision, the exponent is represented in 8-bit biased (excess-127) notation.

Qus : 8 Phrases PYQ

With 4-bit 2's complement arithmetic, which of the following addition will result in overflow?

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Phrases Previous Year PYQ Phrases NIMCET 2019 PYQ

Solution

Qus : 9 Phrases PYQ

If the 2's complement representation of a number is (011010)₂ , what is its equivalent hexadecimal representation?

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Phrases Previous Year PYQ Phrases NIMCET 2019 PYQ

Solution

2's Complement to Hexadecimal Conversion

Given the 2's complement binary number: (011010)
Find its equivalent hexadecimal representation.

Since the number has 6 bits, group the bits into two groups of 4 bits (add leading zeros if needed):
$$ (011010)_2 = (00011010)_2 $$

Now, split into two nibbles (4 bits each):
$$ 0001 \quad 1010 $$

Convert each nibble to hexadecimal:
- $0001_2 = 1_{16}$
- $1010_2 = A_{16}$

Therefore, the hexadecimal representation is: 1A

Qus : 10 Phrases PYQ

The base ( or radix) of the number system such that the following equation holds $\dfrac{312}{20}=13.1$ is

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Phrases Previous Year PYQ Phrases NIMCET 2019 PYQ

Solution

Base (Radix) Problem Solution

Question: Find the base r such that

(312)_r ÷ (20)_r = (13.1)_r

Expansion in base 10

(312)_r = 3r² + 1r + 2
(20)_r = 2r
(13.1)_r = r + 3 + 1/r

Equation

(3r² + r + 2) / (2r) = r + 3 + 1/r

Multiply both sides by 2r

3r² + r + 2 = 2r² + 6r + 2

Simplification

r² - 5r = 0
⇒ r(r - 5) = 0

✅ Final Answer

Since base must be > 1, the valid solution is:
Base (radix) = 5

Qus : 11 Phrases PYQ

Which of the following represents (D4)₁₆?

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Phrases Previous Year PYQ Phrases NIMCET 2019 PYQ

Solution

Qus : 12 Phrases PYQ

A petabyte represents approximately

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Phrases Previous Year PYQ Phrases NIMCET 2011 PYQ

Solution

1 petabyte ≈ 1000 terabytes.

Qus : 13 Phrases PYQ

The least significant bit of the binary number, which is equivalent to any odd decimal number is

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Phrases Previous Year PYQ Phrases NIMCET 2011 PYQ

Solution

Odd numbers always end with LSB = 1.

Qus : 14 Phrases PYQ

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Phrases Previous Year PYQ Phrases NIMCET 2012 PYQ

Solution

Qus : 15 Phrases PYQ

The decimal equivalent to octal 111010 is

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Phrases Previous Year PYQ Phrases NIMCET 2012 PYQ

Solution

Qus : 16 Phrases PYQ

How many bits are required to store an ASCII character?

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Phrases Previous Year PYQ Phrases NIMCET 2008 PYQ

Solution

The standard ASCII code uses 7 bits to represent characters.

Qus : 17 Phrases PYQ

The addition of 4 bit, 2’s Given, √(224)ᵣ = (13)ᵣ, the value of radix r iscomplement binary numbers 1101 and 0100 results in

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Phrases Previous Year PYQ Phrases NIMCET 2008 PYQ

Solution

(13)ᵣ = r + 3

So,

√(224)ᵣ = r + 3

(224)ᵣ = 2r² + 2r + 4

(r + 3)² = 2r² + 2r + 4

r² + 6r + 9 = 2r² + 2r + 4

r² − 4r − 5 = 0

r = 5 (valid radix)

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Phrases Previous Year Questions (PYQs)

Phrases Data Representation - Number System PYQ

Solution

✅ Try values of $n$:

Solution

✅ Given:

✅ Step 1: Normalize the Binary Number

✅ Step 2: Convert the Exponent to Binary

✅ Step 3: Convert the Fraction to 8 Bits

✅ Final Answer:

Solution

Solution

Solution

10-bit 2's Complement Representation of –35

Step-by-Step:

Solution

Problem of 1’s Complement Representation

✅ Conclusion

Solution

IEEE 754 Single Precision Floating Point

? Exponent Representation

✅ Conclusion

Solution

Solution

2's Complement to Hexadecimal Conversion

Solution

Base (Radix) Problem Solution

Expansion in base 10

Equation

Multiply both sides by 2r

Simplification

✅ Final Answer

Solution

Solution

Solution

Solution

Solution

Solution

Solution

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