Boolean algebra. Combinational and sequential circuits. Minimization. Number representations and computer arithmetic (fixed and floating point)

$$\scriptsize{\overset{{\large{\textbf{Mark Distribution in Previous GATE}}}}{\begin{array}{|c|c|c|c|c|c|c|c|}\hline
\textbf{Year}& \textbf{2024-1} & \textbf{2024-2} & \textbf{2023}& \textbf{2022} & \textbf{2021-1}&\textbf{2021-2}&\textbf{Minimum}&\textbf{Average}&\textbf{Maximum}
\\\hline\textbf{1 Mark Count} & 2&2&2&1&2&3&1&2&3
\\\hline\textbf{2 Marks Count} & 2&2&2&2&2&2&2&2&2
\\\hline\textbf{Total Marks} & 6&6&6&5&6&7&\bf{5}&\bf{6}&\bf{7}\\\hline
\end{array}}}$$

Recent questions in Digital Logic

53 votes

3 answers

3121

GATE CSE 2010 | Question: 8
$P$ is a $16$-bit signed integer. The $2$'s complement representation of $P$ is $(F87B)_{16}$. The $2$'s complement representation of $8\times P$ is $(C3D8)_{16}$ $(187B)_{16}$ $(F878)_{16}$ $(987B)_{16}$

$P$ is a $16$-bit signed integer. The $2$'s complement representation of $P$ is $(F87B)_{16}$. The $2$'s complement representation of $8\times P$ is$(C3D8)_{16}$$(187B)_{...

16.5k views

go_editor asked Sep 29, 2014

53 votes

2 answers

3122

GATE CSE 2010 | Question: 7
The main memory unit with a capacity of $4$ $\text{megabytes}$ is built using $1\text{M} \times \text{1-bit}$ DRAM chips. Each DRAM chip has $1\text{K}$ rows of cells with $1\text{K}$ cells in each row. The time taken for a single ... in the memory unit is $100$ nanoseconds $100\times 2^{10}$ nanoseconds $100\times 2^{20}$ nanoseconds $3200\times 2^{20}$ nanoseconds

The main memory unit with a capacity of $4$ $\text{megabytes}$ is built using $1\text{M} \times \text{1-bit}$ DRAM chips. Each DRAM chip has $1\text{K}$ rows of cells wit...

19.0k views

go_editor asked Sep 29, 2014

25 votes

3 answers

3123

GATE CSE 2010 | Question: 6
The minterm expansion of $f(P,Q,R) = PQ +Q \bar{R}+P\bar{R}$ is $m_2+m_4+m_6+m_7$ $m_0+m_1+m_3+m_5$ $m_0+m_1+m_6+m_7$ $m_2+m_3+m_4+m_5$

The minterm expansion of $f(P,Q,R) = PQ +Q \bar{R}+P\bar{R}$ is$m_2+m_4+m_6+m_7$$m_0+m_1+m_3+m_5$$m_0+m_1+m_6+m_7$$m_2+m_3+m_4+m_5$

7.5k views

go_editor asked Sep 29, 2014

25 votes

4 answers

3124

GATE CSE 2011 | Question: 50
Consider the following circuit involving three D-type flip-flops used in a certain type of counter configuration. If at some instance prior to the occurrence of the clock edge, $P, Q$ and $R$ have a value $0$, $1$ and $0$ respectively, what shall be the value of $PQR$ after the clock edge? $000$ $001$ $010$ $011$

Consider the following circuit involving three D-type flip-flops used in a certain type of counter configuration.If at some instance prior to the occurrence of the clock ...

11.3k views

go_editor asked Sep 29, 2014

27 votes

6 answers

3125

GATE CSE 2011 | Question: 15
The minimum number of $\text{D}$ flip-flops needed to design a mod-258 counter is 9 8 512 258

The minimum number of $\text{D}$ flip-flops needed to design a mod-258 counter is98512258

15.2k views

go_editor asked Sep 29, 2014

24 votes

7 answers

3126

GATE CSE 2011 | Question: 14
The simplified SOP (Sum of Product) from the Boolean expression $(P + \bar{Q} + \bar{R}) . (P + \bar{Q} + R) . (P + Q +\bar{R})$ is $(\bar{P}.Q+\bar{R})$ $(P+\bar{Q}.\bar{R})$ $(\bar{P}.Q+R)$ $(P.Q+R)$

The simplified SOP (Sum of Product) from the Boolean expression$$(P + \bar{Q} + \bar{R}) . (P + \bar{Q} + R) . (P + Q +\bar{R})$$ is $(\bar{P}.Q+\bar{R})$$(P+\bar{Q}.\bar...

9.8k views

go_editor asked Sep 29, 2014

22 votes

2 answers

3127

GATE CSE 2011 | Question: 13
Which one of the following circuits is NOT equivalent to a $2$-input $XNOR$ (exclusive $NOR$) gate?

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

5.7k views

go_editor asked Sep 29, 2014

45 votes

7 answers

3128

GATE CSE 2014 Set 3 | Question: 55
Let $\oplus$ denote the exclusive OR (XOR) operation. Let '$1$' and '$0$' denote the binary constants. Consider the following Boolean expression for $F$ over two variables $P$ and $Q$ ... $F$ is $P+Q$ $\overline{P+Q}$ $P \oplus Q$ $\overline {P \oplus Q}$

Let $\oplus$ denote the exclusive OR (XOR) operation. Let '$1$' and '$0$' denote the binary constants. Consider the following Boolean expression for $F$ over two variable...

11.0k views

go_editor asked Sep 28, 2014

27 votes

5 answers

3129

GATE CSE 2014 Set 3 | Question: 45
The above synchronous sequential circuit built using JK flip-flops is initialized with $Q_2Q_1Q_0 = 000$. The state sequence for this circuit for the next $3$ clock cycles is $001, 010, 011$ $111, 110, 101$ $100, 110, 111$ $100, 011, 001$

The above synchronous sequential circuit built using JK flip-flops is initialized with $Q_2Q_1Q_0 = 000$. The state sequence for this circuit for the next $3$ clock cycle...

17.8k views

go_editor asked Sep 28, 2014

29 votes

4 answers

3130

GATE CSE 2014 Set 3 | Question: 8
Consider the following combinational function block involving four Boolean variables $x,\:y,\:a,\:b$ where $x,\:a,\:b$ are inputs and $y$ is the output. f(x, a, b, y) { if(x is 1) y = a; else y = b; } Which one of the following digital logic blocks is the most suitable for implementing this function? Full adder Priority encoder Multiplexor Flip-flop

Consider the following combinational function block involving four Boolean variables $x,\:y,\:a,\:b$ where $x,\:a,\:b$ are inputs and $y$ is the output.f(x, a, b, y) { if...

7.3k views

go_editor asked Sep 28, 2014

18 votes

1 answer

3131

GATE CSE 2014 Set 3 | Question: 7
Consider the following minterm expression for $F$: $F(P,Q,R,S) = \sum 0,2,5,7,8,10,13,15$ The minterms $2$, $7$, $8$ and $13$ are 'do not care' terms. The minimal sum-of-products form for $F$ is $Q \bar S+ \bar QS$ $ \bar Q \bar S+QS$ $ \bar Q \bar R \bar S+ \bar QR \bar S+Q \bar R S+QRS$ $ \bar P \bar Q \bar S+ \bar P QS+PQS+P \bar Q \bar S$

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

4.8k views

go_editor asked Sep 28, 2014

36 votes

5 answers

3132

GATE CSE 2014 Set 2 | Question: 45
The value of a $\text{float}$ type variable is represented using the single-precision $\text{32-bit}$ floating point format of $\text{IEEE-754}$ standard that uses $1$ $\text{bit}$ for sign, $\text{8 bits}$ for biased exponent and ... . The representation of $X$ in hexadecimal notation is $\text{C1640000H}$ $\text{416C0000H}$ $\text{41640000H}$ $\text{C16C0000H}$

The value of a $\text{float}$ type variable is represented using the single-precision $\text{32-bit}$ floating point format of $\text{IEEE-754}$ standard that uses $1$ $\...

11.3k views

go_editor asked Sep 28, 2014

33 votes

3 answers

3133

GATE CSE 2014 Set 2 | Question: 8
Consider the equation $(123)_5=(x8)_y$ with $x$ and $y$ as unknown. The number of possible solutions is _____ .

Consider the equation $(123)_5=(x8)_y$ with $x$ and $y$ as unknown. The number of possible solutions is _____ .

9.6k views

go_editor asked Sep 28, 2014

52 votes

6 answers

3134

GATE CSE 2014 Set 2 | Question: 7
Let $k=2^n$. A circuit is built by giving the output of an $n$-bit binary counter as input to an $n\text{-to-}2^n$ bit decoder. This circuit is equivalent to a $k$-bit binary up counter. $k$-bit binary down counter. $k$--bit ring counter. $k$-bit Johnson counter.

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

19.9k views

go_editor asked Sep 28, 2014

38 votes

3 answers

3135

GATE CSE 2014 Set 2 | Question: 6
The dual of a Boolean function $F(x_1,x_2,\dots,x_n,+, .,')$, written as $F^D$ is the same expression as that of $F$ with $+$ and $⋅$ swapped. $F$ is said to be self-dual if $F = F^D$. The number of self-dual functions with $n$ Boolean variables is $2^n$ $2^{n-1}$ $2^{2^{n}}$ $2^{2^{n-1}}$

The dual of a Boolean function $F(x_1,x_2,\dots,x_n,+, .,')$, written as $F^D$ is the same expression as that of $F$ with $+$ and $⋅$ swapped. $F$ is said to be self-du...

12.5k views

go_editor asked Sep 28, 2014

37 votes

4 answers

3136

GATE CSE 2014 Set 1 | Question: 45
Consider the $4\text{-to-1}$ multiplexer with two select lines $ S_1$ and $ S_0 $ given below The minimal sum-of-products form of the Boolean expression for the output $F$ of the multiplexer is $\bar{P}Q + Q\bar{R} + P\bar{Q}R$ $\bar{P}Q + \bar{P}Q\bar{R} + PQ\bar{R} + P\bar{Q}R$ $\bar{P}QR + \bar{P}Q\bar{R} + Q\bar{R} + P\bar{Q}R$ $PQ\bar{R}$

Consider the $4\text{-to-1}$ multiplexer with two select lines $ S_1$ and $ S_0 $ given below The minimal sum-of-products form of the Boolean expression for the output $F...

13.3k views

go_editor asked Sep 28, 2014

91 votes

7 answers

3137

GATE CSE 2006 | Question: 40
Consider numbers represented in 4-bit Gray code. Let $ h_{3}h_{2}h_{1}h_{0}$ be the Gray code representation of a number $n$ and let $ g_{3}g_{2}g_{1}g_{0}$ be the Gray code of $ (n+1)(modulo 16)$ ... $ g_{3}(h_{3}h_{2}h_{1}h_{0})=\sum (0,1,6,7,10,11,12,13) $

Consider numbers represented in 4-bit Gray code. Let $ h_{3}h_{2}h_{1}h_{0}$ be the Gray code representation of a number $n$ and let $ g_{3}g_{2}g_{1}g_{0}$ be the Gray...

20.7k views

Rucha Shelke asked Sep 26, 2014

54 votes

6 answers

3138

GATE CSE 2006 | Question: 39
We consider the addition of two $2's$ complement numbers $ b_{n-1}b_{n-2}\dots b_{0}$ and $a_{n-1}a_{n-2}\dots a_{0}$. A binary adder for adding unsigned binary numbers is used to add the two numbers. The sum is denoted by $ c_{n-1}c_{n-2}\dots c_{0}$ and the ... $ c_{out}\oplus c_{n-1}$ $ a_{n-1}\oplus b_{n-1}\oplus c_{n-1}$

We consider the addition of two $2's$ complement numbers $ b_{n-1}b_{n-2}\dots b_{0}$ and $a_{n-1}a_{n-2}\dots a_{0}$. A binary adder for adding unsigned binary numbers i...

18.8k views

Rucha Shelke asked Sep 26, 2014

61 votes

4 answers

3139

GATE CSE 2006 | Question: 38
Consider a Boolean function $ f(w,x,y,z)$. Suppose that exactly one of its inputs is allowed to change at a time. If the function happens to be true for two input vectors $ i_{1}=\left \langle w_{1}, x_{1}, y_{1},z_{1}\right \rangle $ ... $ wx\overline{y} \overline{z}, xz, w\overline{x}yz$ $ wx\overline{y}, wyz, wxz, \overline{w}xz, x\overline{y}z, xyz$

Consider a Boolean function $ f(w,x,y,z)$. Suppose that exactly one of its inputs is allowed to change at a time. If the function happens to be true for two input vectors...

21.2k views

Rucha Shelke asked Sep 26, 2014

34 votes

3 answers

3140

GATE CSE 2014 Set 1 | Question: 8
The base (or radix) of the number system such that the following equation holds is____________. $\frac{312}{20} = 13.1$

The base (or radix) of the number system such that the following equation holds is____________. $\frac{312}{20} = 13.1$

12.5k views

go_editor asked Sep 26, 2014

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