Digital Signal Processing

Representation of Numbers

Question 1
Marks : +2 | -2
Pass Ratio : 100%
What is the binary equivalent of (-3/8)?
(10011)2
(0011)2
(1100)2
(1101)2
Explanation:
The number (-3/8) is stored in the computer as the 2’s complement of (3/8)
Question 2
Marks : +2 | -2
Pass Ratio : 100%
What is the largest floating point number that can be represented using a 32-bit word?
3*1038
1.7*1038
0.2*1038
0.3*1038
Explanation:
Let the mantissa be represented by 23 bits plus a sign bit and let the exponent be represented by 7 bits plus a sign bit.
Question 3
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Pass Ratio : 100%
If the two numbers are to be multiplied, the mantissa are multiplied and the exponents are added.
True
False
Explanation:
Let us consider two numbers X=M.2E and Y=N.2F
Question 4
Marks : +2 | -2
Pass Ratio : 100%
For a twos complement representation, the truncation error is ____________
Always positive
Always negative
Zero
None of the mentioned
Explanation:
For a two’s complement representation, the truncation error is always negative and falls in the range
Question 5
Marks : +2 | -2
Pass Ratio : 100%
What is the 2’s complement of (1100)2?
(0100)2
(0011)2
(0111)2
(1100)2
Explanation:
The ones complement of (1100)2 is (0011)2. Thus the two complement of this number is obtained as (0011)2+(0001)2=(0100)2.
Question 6
Marks : +2 | -2
Pass Ratio : 100%
If 0<E<255, then which of the following statement is true about X?
Fractional number
Infinity
Mixed number
Zero
Explanation:
According to the IEEE 754 standard, for a 32-bit machine, single precision floating point number is represented as X=(-1)s.2E-127(M).
Question 7
Marks : +2 | -2
Pass Ratio : 100%
What is the mantissa and exponent respectively obtained when we add 5 and 3/8 in binary float point representation?
0.101010,011
0.101000,011
0.101011,011
0.101011,101
Explanation:
We can represent the numbers in binary float point as
Question 8
Marks : +2 | -2
Pass Ratio : 50%
What is the smallest floating point number that can be represented using a 32-bit word?
3*10-38
2*10-38
0.2*10-38
0.3*10-38
Explanation:
Let the mantissa be represented by 23 bits plus a sign bit and let the exponent be represented by 7 bits plus a sign bit.
Question 9
Marks : +2 | -2
Pass Ratio : 100%
If (101.01)2=(x)10, then what is the value of x?
505.05
10.101
101.01
5.25
Explanation:
(101.01)2=1*22+0*21+1*20+0*2-1+1*2-2=(5.25)10
Question 10
Marks : +2 | -2
Pass Ratio : 100%
What is the resolution to cover a range of numbers xmax-xmin with ‘b’ number of bits?
(xmax+xmin)/(2b-1)
(xmax+xmin)/(2b+1)
(xmax-xmin)/(2b-1)
(xmax-xmin)/(2b+1)
Explanation:
A fixed point representation of numbers allows us to cover a range of numbers, say, xmax-xmin with a resolution