51. A single input single output system and its transpose have identical impulse responses and hence the same input-output relationship.
A. True
B. False
Answer: A
If h(n) is the impulse response of the single input single output system, and h1(n) is the impulse response of the transposed system, then we know that h(n)=h1>(n). Thus, a single input single output system and its transpose have identical impulse responses and hence the same input-output relationship.
52. 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
Answer: D
A closed-form solution of the state space equations is easily obtained when the system matrix F is diagonal. Hence, by finding a matrix P so that F1=PFP-1 is diagonal, the solution of the state equations is simplified considerably.
53. 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
Answer: B
A number λ is an Eigenvalue of F and a nonzero vector U is the associated Eigenvector if
FU=λU
Thus, we obtain (F-λI)U=0.
54. The determinant |F-λI|=0 yields the characteristic polynomial of the matrix F.
A. True
B. False
Answer: A
We know that (F-λI)U=0
The above equation has a nonzero solution U if the matrix F-λI is singular, which is the case if the determinant of (F-λI) is zero. That is, |F-λI|=0.
This determinant yields the characteristic polynomial of the matrix F.
55. The parallel form realization is also known as normal form representation.
A. True
B. False
Answer: A
The parallel form realization is also known as normal form representation, because the matrix F is diagonal, and hence the state variables are uncoupled.
56. 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
Answer: D
If (101.01)2=(x)10, then what is the value of x is
(101.01)2=1*22+0*21+1*20+0*2-1+1*2-2=(5.25)10
=>x=5.25.
57. 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
Answer: A
A real number X can be represented as X=\(\sum_{i=-A}^B b_i r^{-i}\) where bi represents the digit, ‘r’ is the radix or base, A is the number of integer digits, and B is the number of fractional digits.
58. The binary point between the digits b0 and b1 exists physically in the computer.
A. True
B. False
Answer: B
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.
59. 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)
Answer: C
A fixed point representation of numbers allows us to cover a range of numbers, say, xmax-xmin with a resolution
Δ=(xmax-xmin)/(m-1)
where m=2b is the number of levels and ‘b’ is the number of bits.
60. 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
Answer: D
We can represent 5 in binary floating-point as
5=0.625*8=0.625*23
The above number can be represented in binary float point representation as 0.101000*2011
