Jamia Millia Islamia MCA Data Representation - Number System Previous Year Question Paper and Solution with PDF

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Jamia Millia Islamia MCA Data Representation - Number System PYQ

Qus : 1 Jamia Millia Islamia MCA PYQ

The decimal equivalent of $(0.101)_2$ will be —

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Jamia Millia Islamia MCA Previous Year PYQ Jamia Millia Islamia MCA JAMIA MILLIA ISLAMIA MCA 2024 PYQ

Solution

$(0.101)_2 = (1×2^{-1}) + (0×2^{-2}) + (1×2^{-3}) = 0.5 + 0 + 0.125 = 0.625$

Qus : 2 Jamia Millia Islamia MCA PYQ

How many bytes are required to encode 2000 bits of data?

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Jamia Millia Islamia MCA Previous Year PYQ Jamia Millia Islamia MCA JAMIA MILLIA ISLAMIA MCA 2020 PYQ

Solution

1 byte = 8 bits So, $2000 \text{ bits} = \dfrac{2000}{8} = 250$ bytes.

Qus : 3 Jamia Millia Islamia MCA PYQ

The pair byte and nibble comprise of ...... bit(s) respectively.

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Jamia Millia Islamia MCA Previous Year PYQ Jamia Millia Islamia MCA JAMIA MILLIA ISLAMIA MCA 2020 PYQ

Solution

1 byte = 8 bits 1 nibble = 4 bits

Qus : 4 Jamia Millia Islamia MCA PYQ

What is the name of the data metric used to refer to the size $10^{24}$ ?

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Jamia Millia Islamia MCA Previous Year PYQ Jamia Millia Islamia MCA JAMIA MILLIA ISLAMIA MCA 2020 PYQ

Solution

$10^{24}$ bytes = 1 Yottabyte. The prefix "Yotta" represents $10^{24}$.

Qus : 5 Jamia Millia Islamia MCA PYQ

The hexadecimal subtraction of $(56)_{16}$ from $(427)_{16}$ results in:

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Solution

$(427)_{16} - (56)_{16} = (371)_{16}$

Qus : 6 Jamia Millia Islamia MCA PYQ

In which numbering system can the binary number 1011011111000101 be easily converted to?

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Jamia Millia Islamia MCA Previous Year PYQ Jamia Millia Islamia MCA JAMIA MILLIA ISLAMIA MCA 2022 PYQ

Solution

Grouping binary in 4 bits maps directly to hex.

Qus : 7 Jamia Millia Islamia MCA PYQ

$8\,\text{GB}$ is equal to:

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Jamia Millia Islamia MCA Previous Year PYQ Jamia Millia Islamia MCA JAMIA MILLIA ISLAMIA MCA 2019 PYQ

Solution

Zing is not a search engine.

Qus : 8 Jamia Millia Islamia MCA PYQ

Convert (231)_4 into (____)_3.

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Jamia Millia Islamia MCA Previous Year PYQ Jamia Millia Islamia MCA JAMIA MILLIA ISLAMIA MCA 2022 PYQ

Solution

(231)_4 = 2·4^2 + 3·4 + 1 = 45_(10).

45 to base 3 → 1·3^3 + 2·3^2 + 0·3 + 0 = 1200_3.

Qus : 9 Jamia Millia Islamia MCA PYQ

Convert (1278)_12 into (____)_4.

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Jamia Millia Islamia MCA Previous Year PYQ Jamia Millia Islamia MCA JAMIA MILLIA ISLAMIA MCA 2022 PYQ

Solution

(1278)_12 = 1·12^3 + 2·12^2 + 7·12 + 8 = 2108_(10).

2108 to base 4:

= 2·4^5 + 0·4^4 + 0·4^3 + 3·4^2 + 3·4 + 0 = 200330_4.

Qus : 10 Jamia Millia Islamia MCA PYQ

Convert (110100)_2 into (____)_16

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Jamia Millia Islamia MCA Previous Year PYQ Jamia Millia Islamia MCA JAMIA MILLIA ISLAMIA MCA 2022 PYQ

Solution

110100₂ = 0011 0100₂ = 3 4₁₆ →

Qus : 11 Jamia Millia Islamia MCA PYQ

Let A and B be two sets containing 2 elements and 4 elements respectively. The number of subsets of $A \times B$ having 3 or more elements is:

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Jamia Millia Islamia MCA Previous Year PYQ Jamia Millia Islamia MCA JAMIA MILLIA ISLAMIA MCA 2019 PYQ

Solution

$|A| = 2, |B| = 4 \Rightarrow |A \times B| = 8$ Total subsets of 8 elements = $2^8 = 256$ Subsets with less than 3 elements = $1 + 8 + 28 = 37$ Subsets with 3 or more elements = $256 - 37 = 219$

Qus : 12 Jamia Millia Islamia MCA PYQ

Convert the following number to decimal: (1032.2)_4

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Jamia Millia Islamia MCA Previous Year PYQ Jamia Millia Islamia MCA JAMIA MILLIA ISLAMIA MCA 2022 PYQ

Solution

1·4^3 + 0·4^2 + 3·4 + 2 + 2·4^(-1) = 64 + 12 + 2 + 0.5 = 78.5

Qus : 13 Jamia Millia Islamia MCA PYQ

Which of the following is the smallest memory unit?

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Jamia Millia Islamia MCA Previous Year PYQ Jamia Millia Islamia MCA JAMIA MILLIA ISLAMIA MCA 2025 PYQ

Solution

Bit is the smallest unit of data in a computer and can store either 0 or 1.

Qus : 14 Jamia Millia Islamia MCA PYQ

The binary of the decimal number 219 is …

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Jamia Millia Islamia MCA Previous Year PYQ Jamia Millia Islamia MCA JAMIA MCA 2016 PYQ

Solution

Divide 219 by 2 repeatedly: $219_{10} = (11011011)_2$.

Qus : 15 Jamia Millia Islamia MCA PYQ

The Octal equivalent of the Hexadecimal number $(A07)_{16}$ is …

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Jamia Millia Islamia MCA Previous Year PYQ Jamia Millia Islamia MCA JAMIA MCA 2016 PYQ

Solution

Convert $(A07)_{16}$ → binary: $A = 1010,\ 0 = 0000,\ 7 = 0111$ $\Rightarrow (101000000111)_2$. Now group in 3 bits for octal: $(101)(000)(000)(111) = (5007)_8$.

Qus : 16 Jamia Millia Islamia MCA PYQ

If $(27)_5 = 141$, then the missing digit is …

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Jamia Millia Islamia MCA Previous Year PYQ Jamia Millia Islamia MCA JAMIA MCA 2016 PYQ

Solution

$(2x7)_8 = 141_{10} \Rightarrow 2\times8^2 + x\times8 + 7 = 141$. $128 + 8x + 7 = 141 \Rightarrow 8x = 6 \Rightarrow x = \dfrac{6}{8}=0.75$. But $x$ must be a digit (integer), so $x=2$.

Qus : 17 Jamia Millia Islamia MCA PYQ

One nibble is equal to how many bits?

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Jamia Millia Islamia MCA Previous Year PYQ Jamia Millia Islamia MCA JAMIA MILLIA ISLAMIA MCA 2024 PYQ

Solution

1 nibble = 4 bits (half of a byte).

Qus : 18 Jamia Millia Islamia MCA PYQ

The octal equivalent of the binary number $(0010010100)_2$ is —

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Jamia Millia Islamia MCA Previous Year PYQ Jamia Millia Islamia MCA JAMIA MILLIA ISLAMIA MCA 2024 PYQ

Solution

Group binary digits in groups of 3 from right: $(00\ 100\ 101\ 00)_2 = (010\ 010\ 100)_2 = (224)_8$

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