GATE CSE & IT

Consider the following Boolean expression of a function $F$ : $$ F(P, Q)=(\bar{P}+Q) \oplus(\bar{P} Q) $$ Which of the following expressions is/are equivalent to $F$ ?

Consider the 8-bit signed integers $X, Y$ and $Z$ represented using the sign-magnitude form. The binary representations of $X$ and $Y$ are as follows: $$ X: 10110100 \quad Y: 01001...

Which one of the following options is not a property of Boolean Algebra? Note: + is OR operation, • is AND operation, and ' is NOT operation

In a system, numbers are represented using 4-bit two's complement form. Consider four numbers $N 1=1011, N 2=1101, N 3=1010$ and $N 4=1001$ in the system. Which of the following op...

Consider the following 4-variable Boolean function $$ F(A, B, C, D)=\Sigma m(0,1,2,3,8,9,10,11) $$ Consider $A$ as MSB, $D$ as LSB. Which one of the following options represents th...

Consider a Boolean function $F$ with the following minterm expression: $$ F(P, Q, R, S)=\Sigma m(1,2,3,4,5,7,10,12,13,14) $$ Which of the following options is/are the minimal sum-o...

Consider a 2-bit saturating up/down counter that performs the saturating up count when the input $P$ is 0 , and the saturating down count when $P$ is 1 . The Next State table of th...

The 32-bit IEEE 754 single precision representation of a number is 0xC2710000. The number in decimal representation is $\_\_\_\_$ . (rounded off to two decimal places)

The number -6 can be represented as 1010 in 4-bit 2's complement representation. Which of the following is/are CORRECT 2's complement representation(s) of $-6$ ?

Consider the following four variable Boolean function in sum-of-product form $$F\left(b_3, b_2, b_1, b_0\right)=\Sigma(0,2,4,8,10,11,12)$$ where the value of the function is comput...

Let $X$ be a 3-variable Boolean function that produces output as ' 1 ' when at least two of the input variables are ' 1 '. Which of the following statement(s) is/are CORRECT, where...

In a 4-bit ripple counter, if the period of the waveform at the last flip-flop is 64 microseconds, then the frequency of the ripple counter in kHz is _________. (Answer in integer)

The following two signed 2's complement numbers (multiplicand M and multiplier Q ) are being multiplied using Booth's algorithm : M : 1100110111101101 and Q : 1010010010101010 The...

Which of the following Boolean algebraic equation(s) is/are CORRECT?

Three floating point numbers $X, Y$, and $Z$ are stored in three registers $R_X, R_Y$, and $R_Z$, respectively in IEEE 754 single precision format as given below in hexadecimal: $$...

Consider a system that uses 5 bits for representing signed integers in 2’s complement format. In this system, two integers A and B are represented as A =01010 and B =11010. Which o...

Consider a Boolean expression given by $F(X, Y, Z) = \Sigma(3,5,6,7)$. Which of the following statements is/are CORRECT?

The format of a single-precision floating-point number as per the IEEE 754 standard is: Sign (1 bit) Exponent (8 bits) Mantissa (23 bits) Choose the largest floating-point number a...

For a Boolean variable x, which of the following statements is/are FALSE?

Which of the following is/are EQUAL to 224 in radix-5 (i.e., base-5) notation?

A particular number is written as 132 in radix-4 representation. The same number in radix-5 representation is ____________.

Consider the IEEE-754 single precision floating point numbers P=0xC1800000 and Q=0x3F5C2EF4. Which one of the following corresponds to the product of these numbers (i.e., P $$\time...

Let R1 and R2 be two 4-bit registers that store numbers in 2's complement form. For the operation R1 + R2, which one of the following values of R1 and R2 gives an arithmetic overfl...

Let the representation of a number in base 3 be 210. What is the hexadecimal representation of the number?

Which one of the following circuits implements the Boolean function given below? f(x, y, z) = m 0 + m 1 + m 3 + m 4 + m 5 + m 6 , where m i is the i th minterm.

Suppose we want to design a synchronous circuit that processes a string of 0’s and 1’s. Given a string, it produces another string by replacing the first 1 in any subsequence of co...

Consider the following Boolean expression. $$F = (X + Y + Z)(\overline X + Y)(\overline Y + Z)$$ Which of the following Boolean expressions is/are equivalent to $$\overline F$$ (co...

Consider the following representation of a number in IEEE 754 single-precision floating point format with a bias of 127. S: 1 E: 10000001 F : 11110000000000000000000 Here S, E and...

If x and y are two decimal digits and (0.1101) 2 = (0.8xy5) 10 , the decimal value of x + y is ______

The format of the single-precision floating-point representation of a real number as per the IEEE 754 standard is as follows: sign exponent mantissa Which one of the following choi...

Consider a Boolean function f(w, x, y, z) such that f(w, 0, 0, z) = 1 f(1, x, 1, z) = x + z f(w, 1, y, z) = wz + y The number of literals in the minimal sum-of-products expression...

Consider three registers R1, R2 and R3 that store numbers in IEEE-754 single precision floating point format. Assume that R1 and R2 contain the values (in hexadecimal notation) 0x4...

A multiplexer is placed between a group of 32 registers and an accumulator to regulate data movement such that at any given point in time the content of only one register will move...

If there are m input lines and n output lines for a decoder that is used to uniquely address a byte addressable 1 KB RAM, then the minimum value of m + n is ____.

In 16-bit 2's complement representation, the decimal number -28 is :

Which one of the following is NOT a valid identity?

Consider Z = X - Y, where X, Y and Z are all in sign-magnitude form. X and Y are each represented in n bits. To avoid overflow, the representation of Z would require a minimum of :

What is the minimum number of 2-input NOR gates required to implement a 4-variable function function expressed in sum-of-minterms form as f = Σ(0, 2, 5, 7, 8, 10, 13, 15)? Assume t...

Consider the unsigned $$8$$-bit fixed point binary number representation below $$${b_7}\,\,{b_6}\,\,{b_5}\,\,{b_4}\,\,{b_3}\,\,.\,\,{b_2}\,\,{b_1}\,\,{b_0}$$$ where the position of...

Consider the minterm list form of a Boolean function 𝐹 given below. $$F\left( {P,Q,R,S} \right) = $$ $$\sum {m\left( {0,2,5,7,9,11} \right)} $$ $$ + \,\,d\left( {3,8,10,12,14} \ri...

Let $$ \oplus $$ and $$ \odot $$ denote the Exclusive OR and Exclusive NOR operations, respectively. Which one of the following is NOT CORRECT?

The $n$-bit fixed-point representation of an unsigned real number $X$ uses $f$ bits for the fraction part. Let $i=n-f$. The range of decimal values for $X$ in this representation i...

Let $$X$$ be the number of distinct $$16$$-bit integers in $$2’s$$ complement representation. Let $$Y$$ be the number of distinct $$16$$-bit integers in sign magnitude representati...

Let, $${x_1} \oplus {x_2} \oplus {x_3} \oplus {x_4} = 0$$ where $${x_1},\,{x_2},\,{x_3},\,{x_4}$$ are Boolean Variables, and $$ \oplus $$ is the $$XOR$$ operator. Which one of the...

Consider a carry lookahead adder for adding two $$n$$-bit integers, built using gates of fan-in at most two. The time to perform addition using this adder is

We want to design a synchronous counter that counts the sequence $$0-1-0-2-0-3$$ and then repeats. The minimum number of $$J-K$$ flip-flops required to implement this counter is __...

Consider the Boolean operator $$ \ne $$ with the following properties: $$x \ne 0 = x,\,\,x \ne 1 = \overline x ,\,\,x \ne x = 0$$ and $$x \ne \overline x = 1.$$ Then $$x \ne y$$ is...

The $$16$$-bit $$2’s$$ complement representation of an integer is $$1111$$ $$1111$$ $$1111$$ $$0101;$$ its decimal representation is ____________.

Consider an eight-bit ripple-carry adder for computing the sum of $$A$$ and $$B,$$ where $$A$$ and $$B$$ are integers represented in $$2’s$$ complement form. If the decimal value o...

A half adder is implemented with $$XOR$$ and $$AND$$ gates. A full adder is implemented with two half adders and one $$OR$$ gate. The propagation delay of an $$XOR$$ gate is twice...

The total number of prime implicants of the function $$f\left( {w,x,y,z} \right) = \sum {\left( {0,2,4,5,6,10} \right)} $$ _________________.

The minimum number of $$JK$$ flip-flops required to construct a synchronous counter with the count sequence $$\left( {0,0,1,1,2,2,3,3,0,0,...} \right)$$ is ____________.

A positive edge-triggered D flip-flop is connected to a positive edge-triggered JK flip-flop as follows. The Q output of the D flip-flop is connected to both the J and K inputs of...

Consider the equation $${\left( {43} \right)_x} = {\left( {y3} \right)_8}$$ where $$x$$ and $$y$$ are unknown. The number of possible solutions is ______________

The number of min-terms after minimizing the following Boolean expression is _______________ . $$$\left[ {D' + AB' + A'C + AC'D + A'C'D} \right]'$$$

Consider a 4-bit Johnson counter with an initial value of 0000. The counting sequence of this counter is

Given the function $$F = P′ + QR,$$ where $$F$$ is a function in three Boolean variables $$P,Q$$ and $$R$$ and $$P'=!P,$$ consider the following statements. $$\eqalign{ & \,\,\,\,\...

Let $$ \ne $$ be a binary operator defined as $$X \ne Y = X' + Y'$$ where $$𝑋$$ and $$𝑌$$ are Boolean variables. Consider the following two statements. $$$\eqalign{ & \left( {S1}...

The binary operator $$ \ne $$ is defined by the following truth table. p q p$$ \ne $$q 0 0 0 0 1 1 1 0 1 1 1 0 Which one of the following is true about the binary operator $$ \ne $...

Consider the operations $$f\left( {x,y,z} \right) = X'YZ + XY' + Y'Z'$$ and $$g\left( {x,y,z} \right) = X'YZ + X'YZ' + XY$$. Which one of the following is correct?

The base (or radix) of the number system such that the following equation holds is __________ $${{312} \over {20}} = 13.1$$

Let $$ \oplus $$ denote the exclusive $$OR\left( {XOR} \right)$$ operation. Let $$'1'$$ and $$'0'$$ denote the binary constants. Consider the following Boolean expression for $$F$$...

Consider the following interm expression of $$F:$$ $$F\left( {P,\,Q,\,R,\,S} \right) = \sum {0,2,5,7,8,10,13,15} $$ The minterms $$2, 7, 8$$ and $$13$$ are 'do not care' terms. The...

Consider the following Boolean expression for $$F:$$ $$F\left( {P,\,Q,\,R,\,S} \right) = PQ + \overline P QR + \overline P Q\overline R S.$$ The minimal sum-of-products form of $$F...

The dual of a Boolean function $$F\left( {{x_1},{x_2},\,....,\,{x_n},\, + , \cdot ,'} \right),$$ written as $${F^D}$$, is the same expression as that of $$F$$ with $$+$$ and $$ \cd...

Consider the equation $${\left( {123} \right)_5} = {\left( {x8} \right)_y}$$ with $$x$$ and $$y$$ as unknown. The number of possible solutions is _________.

Let $$k = {2^n}.$$ A circuit is built by giving the output of an ݊$$n$$-bit binary counter as input to an $$n$$-to-$${2^n}$$ bit decoder. This circuit is equivalent to a

Which one of the following expressions does NOT represent exclusive NOR of $$x$$ and $$y?$$

The smallest integer that can be represented by an $$8$$-bit number in $$2's$$ complement form is

The simplified $$SOP$$ (Sum of product) form of the Boolean expression $$\left( {P + \overline Q + \overline R } \right).\left( {P + \overline Q + R} \right).\left( {P + Q + \overl...

Which one of the following circuits is NOT equivalent to a $$2$$-input $$XNOR$$ (exclusive NOR ) gate

The minters expansion of $$f\left( {P,Q,R} \right) = PQ + Q\overline R + P\overline R $$ is

$$P$$ is a $$16$$-bit signed integer. The $$2's$$ complement representtation of $$P$$ is $${\left( {F87B} \right)_{16}}$$ . The $$2's$$ complement representation of $$8{}^ * \,P$$...

What is the minimum number of gates required to implement the Boolean function $$(AB+C)$$ if we have to use only $$2$$-input NOR gates?

$${\left( {1217} \right)_8}$$ is equivalent to

If $$P, Q, R$$ are Boolean variables, then $$\left( {P + \overline Q } \right)$$ $$\left( {P.\overline Q + P.R} \right)\left( {\overline P .\overline R + \overline Q } \right)$$ Si...

Consider the following Boolean function with four variables $$F\left( {w,\,x,\,y,\,z} \right) = \sum {\left( {1,\,3,\,4,\,6,\,9,\,11,\,12,\,14} \right)} $$ the function is

Suppose only one multiplexer and one inverter are allowed to be used to implement any Boolean function of $$n$$ variables. What is the minimum size of the multiplexer needed?

Let $$f\left( {w,x,y,z} \right) = \sum {\left( {0,4,5,7,8,9,13,15} \right).} $$ Which of the following expressions are NOT equivalent to $$f?$$ $$(P)\,\,\,$$ $$x'y'z' + w'xy' + wy'...

How many $$3$$ to $$8$$ decodes with an enable input are needed to construct to constant $$6$$ to $$64$$ line decoder without using any other logic gates