UGC NET Computer Science Data Representation - Number System Previous Year Questions (PYQs)
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Showing 4 questions
The least values of a signed and unsigned data type variables requiring 8 bits, would be:
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Solution
For 8-bit signed integer (two’s complement):
Range = $-2^{7}$ to $2^{7}-1$
Least value = $-128$
For 8-bit unsigned integer:
Range = $0$ to $2^{8}-1$
Least value = $0$
What is the $(4+4)$ bit binary fixed point equivalent of $-(3.72)_{10}$?
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Solution
First convert positive $3.72$ approximately in $(4+4)$ fixed point form.
$3.72 \approx 3.75$
$3 = 0011$
$0.75 = .1100$
So,
$3.75 = 0011.1100$
For negative number, take 2’s complement:
$0011.1100 \to 1100.0100$
Suppose you have eight black and white images taken with a $1$-megapixel camera and one $8$-color image taken by an $8$-megapixel camera. How much hard disk space in total do you need to store these images on your computer?
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Solution
A black and white image needs $1$ bit per pixel.
Size of one $1$-megapixel black and white image $=1\times 10^6$ bits.
Size of $8$ such images $=8\times 10^6$ bits $=1\ MB$.
An $8$-color image needs $\log_2 8=3$ bits per pixel.
Size of one $8$-megapixel $8$-color image $=8\times 10^6\times 3=24\times 10^6$ bits $=3\ MB$.
Total space $=1\ MB+3\ MB=4\ MB$.
Size of one $1$-megapixel black and white image $=1\times 10^6$ bits.
Size of $8$ such images $=8\times 10^6$ bits $=1\ MB$.
An $8$-color image needs $\log_2 8=3$ bits per pixel.
Size of one $8$-megapixel $8$-color image $=8\times 10^6\times 3=24\times 10^6$ bits $=3\ MB$.
Total space $=1\ MB+3\ MB=4\ MB$.
Consider the given number $(45)_y$ where $y$ is the base of the number. Some of the possible values of $y$ are given below.
(A) 5
(B) 6
(C) 7
(D) 8
Choose the correct answer from the options given below :
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Solution
In base $y$, digits must be less than base.
Number $(45)_y$ has digit 5.
Thus
$y>5$
Possible bases:
$6,7,8,\dots$
Given options:
6, 7, 8
Thus
(B), (C), (D)
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