# Number Representation

This set of Digital Signal Processing Multiple Choice Questions & Answers (MCQs) focuses on “Representation of Numbers-1”.

1. If (101.01)2=(x)10, then what is the value of x?
a) 505.05
b) 10.101
c) 101.01
d) 5.25

2. If X is a real number with ‘r’ as the radix, A is the number of integer digits and B is the number of fraction digits, then X=∑Bi=−Abir−i.
a) True
b) False

3. The binary point between the digits b0 and b1 exist physically in the computer.
a) True
b) False

4. What is the resolution to cover a range of numbers xmax-xmin with ‘b’ number of bits?
a) (xmax+xmin)/(2b-1)
b) (xmax+xmin)/(2b+1)
c) (xmax-xmin)/(2b-1)
d) (xmax-xmin)/(2b+1)

5. What are the mantissa and exponent required respectively to represent ‘5’ in binary floating point representation?
a) 011,0.110000
b) 0.110000,011
c) 011,0.101000
d) 0.101000,011

6. If the two numbers are to be multiplied, the mantissa are multiplied and the exponents are added.
a) True
b) False

7. What is the smallest floating point number that can be represented using a 32-bit word?
a) 3*10-38
b) 2*10-38
c) 0.2*10-38
d) 0.3*10-38

8. If 0<E<255, then which of the following statement is true about X?
a) Fractional number
b) Infinity
c) Mixed number
d) Zero

9. For a twos complement representation, the truncation error is ____________
a) Always positive
b) Always negative
c) Zero
d) None of the mentioned

10. Due to non-uniform resolution, the corresponding error in a floating point representation is proportional to the number being quantized.
a) True
b) False

11. What is the binary equivalent of (-3/8)?
a) (10011)2
b) (0011)2
c) (1100)2
d) (1101)2

12. Which of the following is the correct representation of a floating point number X?
a) 2E
b) M.2E(1/2<M<1)
c) 2M.2E(1/2<M<1)
d) None of the mentioned

13. What is the mantissa and exponent respectively obtained when we add 5 and 3/8 in binary float point representation?
a) 0.101010,011
b) 0.101000,011
c) 0.101011,011
d) 0.101011,101

14. What is the largest floating point number that can be represented using a 32-bit word?
a) 3*1038
b) 1.7*1038
c) 0.2*1038
d) 0.3*1038

15. If E=0 and M=0, then which of the following statement is true about X?
a) Not a number
b) Infinity
c) Defined
d) Zero

16. The truncation error for the sign magnitude representation is symmetric about zero.
a) True
b) False

17. What is the range of round-off error for a foxed point representation?
a) [-0.5(2-b+2-bm), 0.5(2-b+2-bm)]
b) [0, (2-b+2-bm)]
c) [0, (2-b-2-bm)]
d) [-0.5(2-b-2-bm), 0.5(2-b-2-bm-bm)]

18. What is the 2’s complement of (1100)2?
a) (0100)2
b) (0011)2
c) (0111)2
d) (1100)2

19. The binary digit b-A is called as ______________
a) LSB
b) Total value
c) MSB
d) None of the mentioned

20. If E=255 and M≠0, then which of the following statement is true about X?
a) Not a number
b) Infinity
c) Defined
d) Zero