Jamia Millia Islamia MCA Data Representation - Number System Previous Year Questions (PYQs) – Page 2 of 2
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Showing 18 questions
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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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 = $256 - 37 = 219$
Convert the following number to decimal: (1032.2)_4
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Solution
1·4^3 + 0·4^2 + 3·4 + 2 + 2·4^(-1) = 64 + 12 + 2 + 0.5 = 78.5
Which of the following is the smallest memory unit?
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Solution
Bit is the smallest unit of data in a computer and can store either 0 or 1.
The binary of the decimal number 219 is …
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Solution
Divide 219 by 2 repeatedly:
$219_{10} = (11011011)_2$.
The Octal equivalent of the Hexadecimal number $(A07)_{16}$ is …
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Solution
Convert $(A07)_{16}$ → binary:
$A = 1010,\ 0 = 0000,\ 7 = 0111$
$\Rightarrow (101000000111)_2$.
Now group in 3 bits for octal: $(101)(000)(000)(111) = (5007)_8$.
If $(27)_5 = 141$, then the missing digit is …
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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 $x=2$.
One nibble is equal to how many bits?
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Solution
1 nibble = 4 bits (half of a byte).
The octal equivalent of the binary number $(0010010100)_2$ is —
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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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