Digital Signal Processing

Representation of Numbers

Question 1
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 2
Marks : +2 | -2
Pass Ratio : 100%
If E=0 and M=0, then which of the following statement is true about X?
Not a number
Infinity
Defined
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 3
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
Question 4
Marks : +2 | -2
Pass Ratio : 100%
What are the mantissa and exponent required respectively to represent ‘5’ in binary floating point representation?
011,0.110000
0.110000,011
011,0.101000
0.101000,011
Explanation:
We can represent 5 as
Question 5
Marks : +2 | -2
Pass Ratio : 100%
If E=255 and M≠0, then which of the following statement is true about X?
Not a number
Infinity
Defined
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 6
Marks : +2 | -2
Pass Ratio : 100%
Due to non-uniform resolution, the corresponding error in a floating point representation is proportional to the number being quantized.
True
False
Explanation:
In floating point representation, the mantissa is either rounded or truncated. Due to non-uniform resolution, the corresponding error in a floating point representation is proportional to the number being quantized.
Question 7
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 8
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 9
Marks : +2 | -2
Pass Ratio : 100%
The binary point between the digits b0 and b1 exist physically in the computer.
True
False
Explanation:
The binary point between the digits b0 and b1 does not exist physically in the computer. Simply, the logic circuits of the computer are designed such that the computations result in numbers that correspond to the assumed location of this point.
Question 10
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)