GATE IT 2006

Question 31

Let L be a context-free language and M a regular language. Then the language L ∩ M is

• always regular
• never regular
• always a deterministic context-free language
• always a context-free language

Question 32

Consider the pushdown automaton (PDA) below which runs over the input alphabet (a, b, c). It has the stack alphabet {Z₀, X} where Z₀ is the bottom-of-stack marker. The set of states of the PDA is (s, t, u, f} where s is the start state and f is the final state. The PDA accepts by final state. The transitions of the PDA given below are depicted in a standard manner. For example, the transition (s, b, X) → (t, XZ₀) means that if the PDA is in state s and the symbol on the top of the stack is X, then it can read b from the input and move to state t after popping the top of stack and pushing the symbols Z₀ and X (in that order) on the stack.
(s, a, Z₀) → (s, XXZ₀)
(s, ϵ, Z₀) → (f, ϵ)
(s, a, X) → (s, XXX)
(s, b, X) → (t, ϵ)
(t, b, X) → (t,.ϵ)
(t, c, X) → (u, ϵ)
(u, c, X) → (u, ϵ)
(u, ϵ, Z₀) → (f, ϵ)
The language accepted by the PDA is

• {a^lb^mcⁿ | l = m = n}
• {a^lb^mcⁿ | l = m}
• {a^lb^mcⁿ | 2l = m+n}
• {a^lb^mcⁿ | m=n}

Question 33

In the context-free grammar below, S is the start symbol, a and b are terminals, and ϵ denotes the empty string.
S → aSAb | ϵ
A → bA | ϵ
The grammar generates the language

• ((a + b)* b)*
• {a^mbⁿ | m ≤ n}
• {a^mbⁿ | m = n}
• a* b*

Question 34

The boolean function for a combinational circuit with four inputs is represented by the following Karnaugh map.

Which of the product terms given below is an essential prime implicant of the function?

• QRS
• PQS
• PQ\'S\'
• Q\'S\'

Question 35

The majority function is a Boolean function f(x, y, z) that takes the value 1 whenever a majority of the variables x, y, z and 1. In the circuit diagram for the majority function shown below, the logic gates for the boxes labeled P and Q are, respectively,

• XOR, AND
• XOR, XOR
• OR, OR
• OR, AND

Question 36

For a state machine with the following state diagram the expression for the next state S+ in terms of the current state S and the input variables x and y is

• S⁺ = S\' . y\' + S . x
• S⁺ =S. x . y\' + S\' . y . x\'
• S⁺ =x . y\'
• S⁺ =S\' . y + S . x\'

Question 37

When multiplicand Y is multiplied by multiplier X = xn - 1xn-2 ....x0 using bit-pair recoding in Booth\'s algorithm, partial products are generated according to the following table. The partial products for rows 5 and 8 are

• 2Y and Y
• -2Y and 2Y
• -2Y and 0
• 0 and Y

Question 38

Which of the following statements about relative addressing mode is FALSE?

• It enables reduced instruction size

• It allows indexing of array elements with same instruction

• It enables easy relocation of data

• It enables faster address calculations than absolute addressing

Question 39

The memory locations 1000, 1001 and 1020 have data values 18, 1 and 16 respectively before the following program is executed.<br> MOVI         Rs, 1                     ; Move immediate <br> LOAD        Rd, 1000(Rs)     ; Load from memory<br> ADDI         Rd, 1000             ; Add immediate<br> STOREI    0(Rd), 20            ; Store immediate<br> Which of the statements below is TRUE after the program is executed ?

• Memory location 1000 has value 20
• Memory location 1020 has value 20
• Memory location 1021 has value 20
• Memory location 1001 has value 20

Question 40

The data path shown in the figure computes the number of 1s in the 32-bit input word corresponding to an unsigned even integer stored in the shift register.
The unsigned counter, initially zero, is incremented if the most significant bit of the shift register is

The micro-program for the control is shown in the table below with missing control words for micro-instructions I₁, I₂, ..... I_n.

The counter width (k), the number of missing micro-instructions (n), and the control word for microinstructions I₂, ..... I_n are, respectively,

• 32, 5, 010
• 5, 32, 010
• 5, 31, 011
• 5, 31, 010