1. The state-space or the internal description of the system still involves a relationship between the input and output signals, what is the additional set of variables it also involves?

A. System variables

B. Location variables

C. State variables

D. None of the mentioned

2. State variables provide information about all the internal signals in the system.

A. True

B. False

3. Which of the following gives the complete definition of the state of a system at time n0?

A. Amount of information at n0 determines output signal for n≥n0

B. Input signal x(n) for n≥n0 determines output signal for n≥n0

C. Input signal x(n) for n≥0 determines output signal for n≥n0

D. Amount of information at n0+input signal x(n) for n≥n0 determines output signal for n≥n0

4. From the definition of the state of a system, the system consists of only one component called memoryless component.

A. True

B. False

5. If we interchange the rows and columns of the matrix F, then the system is called as ______________

A. Identity system

B. Diagonal system

C. Transposed system

D. None of the mentioned

6. A single input single output system and its transpose have identical impulse responses and hence the same input-output relationship.

A. True

B. False

7. A closed-form solution of the state space equations is easily obtained when the system matrix F is?

A. Transpose

B. Symmetric

C. Identity

D. Diagonal

8. What is the condition to call a number λ an Eigenvalue of F and a nonzero vector U is the associated Eigenvector?

A. (F+λI)U=0

B. (F-λI)U=0

C. F-λI=0

D. None of the mentioned

9. The determinant |F-λI|=0 yields the characteristic polynomial of the matrix F.

A. True

B. False

10. The parallel form realization is also known as normal form representation.

A. True

B. False

11. 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

12. 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=\(\sum_{i=-A}^B b_i r^{-i}\).

A. True

B. False

13. The binary point between the digits b0 and b1 exists physically in the computer.

A. True

B. False

14. 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)

15. 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

16. If the two numbers are to be multiplied, the mantissa is multiplied and the exponents are added.

A. True

B. False

17. 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}

18. If 0<E<255, then which of the following statement is true about X?

B. Infinity

C. Mixed number

D. Zero

19. For a twos complement representation, the truncation error is _________

A. Always positive

B. Always negative

C. Zero

D. None of the mentioned

20. Due to non-uniform resolution, the corresponding error in a floating-point representation is proportional to the number being quantized.

A. True

B. False

21. What is the binary equivalent of (-3/8)?

A. (10011)_{2}

B. (0011)_{2}

C. (1100)_{2}

D. (1101)_{2}

22. Which of the following is the correct representation of a floating-point number X?

A. 2^{E}

B. M.2^{E}(1/2<m<1)

C. 2M.2^{E}(1/2<m<1)

D. None of the mentioned

23. 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