Digital Logic & Number representation

Question 41

Consider numbers represented in 4-bit gray code. Let h3h2h1h0 be the gray code representation of a number n and let g3g2g1g0 be the gray code of (n + 1) (modulo 16) value of the number. Which one of the following functions is correct? A: [Tex]g_{0}(h_{3},h_{2},h_{1},h_{0})=\\sum (1,2,3,6,10,13,14,15)[/Tex] B: [Tex]g_{1}(h_{3},h_{2},h_{1},h_{0})=\\sum (4,9,10,11,12,13,14,15)[/Tex] C: [Tex]g_{2}(h_{3},h_{2},h_{1},h_{0})=\\sum (2,4,5,6,7,12,13,15)[/Tex] D: [Tex]g_{3}(h_{3},h_{2},h_{1},h_{0})=\\sum (0,1,6,7,10,11,12,13)[/Tex]

• A

• B

• C

• D

Question 42

Consider the following circuit. Which one of the following is TRUE?

• f is independent of X
• f is independent of Y
• f is independent of Z
• None of X, Y, Z is redundant

Question 43

The hexadecimal representation of 657₈ is

• 1AF
• D78
• D71
• 32F

Question 44

The switching expression corresponding to f(A, B, C, D) = Σ (1, 4, 5, 9, 11, 12) is

• BC\'D\' + A\'C\'D + AB\'D

• ABC\' + ACD + B\'C\'D

• ACD\' + A\'BC\' + AC\'D\'

• A\'BD + ACD\' + BCD\'

Question 45

Consider the following circuit involving a positive edge triggered D FF.

Consider the following timing diagram. 
Let Ai represent the logic level on the line A in the i-th clock period. 
 Let A\' represent the complement of A. The correct output sequence on Y over the clock periods 1 through 5 is

• A0 Al A1\' A3 A4

• A0 Al A2\' A3 A4

• Al A2 A2\' A3 A4

• Al A2\' A3 A4 A5\'

Question 46

Consider the following circuit.

The flip-flops are positive edge triggered D FFs. Each state is designated as a two bit string Q0Q1. Let the initial state be 00. The state transition sequence is:

 A)  
B) 
C)
D)

• A

• B

• C

• D

Question 47

Consider the following floating point format

[caption width="800"] [/caption]

Mantissa is a pure fraction in sign-magnitude form. The decimal number 0.239 × 2

¹³

has the following hexadecimal representation (without normalization and rounding off :

• 0D 24

• 0D 4D

• 4D 0D

• 4D 3D

Question 48

Consider the following floating point format

[caption width="800"] [/caption]

Mantissa is a pure fraction in sign-magnitude form. The normalized representation for the above format is specified as follows. The mantissa has an implicit 1 preceding the binary (radix) point. Assume that only 0\'s are padded in while shifting a field. The normalized representation of the above number (0.239 × 2

¹³

) is:

• 0A 20

• 11 34

• 4D D0

• 4A E8

Question 49

The Boolean function x\'y\' + xy + x\'y is equivalent to

• x\' + y\'
• x + y
• x + y\'
• x\' + y

Question 50

In an SR latch made by cross-coupling two NAND gates, if both S and R inputs are set to 0, then it will result in

• Q = 0, Q\' = 1

• Q = 1, Q\' = 0

• Q = 1, Q\' = 1

• Indeterminate states