Recent questions tagged digital-logic / GATE Overflow for GATE CSE

27 votes

6 answers

2311

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

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15.2k views

go_editor asked Sep 29, 2014

24 votes

7 answers

2312

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...

go_editor

9.8k views

go_editor asked Sep 29, 2014

22 votes

2 answers

2313

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?

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5.7k views

go_editor asked Sep 29, 2014

45 votes

7 answers

2314

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...

go_editor

11.0k views

go_editor asked Sep 28, 2014

27 votes

5 answers

2315

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...

go_editor

17.8k views

go_editor asked Sep 28, 2014

29 votes

4 answers

2316

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...

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7.3k views

go_editor asked Sep 28, 2014

18 votes

1 answer

2317

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-...

go_editor

4.8k views

go_editor asked Sep 28, 2014

24 votes

2 answers

2318

GATE CSE 2014 Set 3 | Question: GA-10
Consider the equation: $(7526)_8 − (Y)_8 = (4364)_8$, where $(X)_N$ stands for $X$ to the base $N$. Find $Y$. $1634$ $1737$ $3142$ $3162$

Consider the equation: $(7526)_8 − (Y)_8 = (4364)_8$, where $(X)_N$ stands for $X$ to the base $N$. Find $Y$.$1634$$1737$$3142$$3162$

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5.6k views

go_editor asked Sep 28, 2014

36 votes

5 answers

2319

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 $1$ $\...

go_editor

11.4k views

go_editor asked Sep 28, 2014

33 votes

3 answers

2320

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 _____ .

go_editor

9.6k views

go_editor asked Sep 28, 2014

52 votes

6 answers

2321

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...

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19.9k views

go_editor asked Sep 28, 2014

38 votes

3 answers

2322

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...

go_editor

12.5k views

go_editor asked Sep 28, 2014

37 votes

4 answers

2323

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...

go_editor

13.3k views

go_editor asked Sep 28, 2014

91 votes

7 answers

2324

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...

Rucha Shelke

20.8k views

Rucha Shelke asked Sep 26, 2014

54 votes

6 answers

2325

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...

Rucha Shelke

18.8k views

Rucha Shelke asked Sep 26, 2014

61 votes

4 answers

2326

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...

Rucha Shelke

21.2k views

Rucha Shelke asked Sep 26, 2014

34 votes

3 answers

2327

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____________. $\frac{312}{20} = 13.1$

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12.5k views

go_editor asked Sep 26, 2014

27 votes

7 answers

2328

GATE CSE 2014 Set 1 | Question: 7
Consider the following Boolean expression for F: $F(P,Q,R,S)= PQ + \bar{P}QR + \bar{P}Q\bar{R}S$ The minimal sum$-$of$-$products form of $F$ is $PQ+QR+QS$ $P+Q+R+S$ $\bar{P} + \bar{Q}+ \bar{R}+ \bar{S}$ $\bar{P}R + \bar{R} \bar{P}S+P$

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

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8.6k views

go_editor asked Sep 26, 2014

23 votes

3 answers

2329

GATE CSE 1998 | Question: 16
Design a synchronous counter to go through the following states:$1, 4, 2, 3, 1, 4, 2, 3, 1, 4 \dots $

Design a synchronous counter to go through the following states:$$1, 4, 2, 3, 1, 4, 2, 3, 1, 4 \dots $$

Kathleen

5.2k views

Kathleen asked Sep 26, 2014

23 votes

2 answers

2330

GATE CSE 1998 | Question: 5
The implication gate, shown below has two inputs ($x \text{ and }y)$; the output is 1 except when $x =1 \text{ and } y=0\text{, realize }f=\bar{x}y+x\bar{y}$ using only four implication gates. Show that the implication gate is functionally complete.

The implication gate, shown below has two inputs ($x \text{ and }y)$; the output is 1 except when $x =1 \text{ and } y=0\text{, realize }f=\bar{x}y+x\bar{y}$ using only f...

Kathleen

3.9k views

Kathleen asked Sep 25, 2014

31 votes

3 answers

2331

GATE CSE 1998 | Question: 2.20
Suppose the domain set of an attribute consists of signed four digit numbers. What is the percentage of reduction in storage space of this attribute if it is stored as an integer rather than in character form? $\text{80%}$ $\text{20%}$ $\text{60%}$ $\text{40%}$

Suppose the domain set of an attribute consists of signed four digit numbers. What is the percentage of reduction in storage space of this attribute if it is stored as an...

Kathleen

7.0k views

Kathleen asked Sep 25, 2014

22 votes

3 answers

2332

GATE CSE 1998 | Question: 2.8
Which of the following operations is commutative but not associative? AND OR NAND EXOR

Which of the following operations is commutative but not associative?ANDORNANDEXOR

Kathleen

9.2k views

Kathleen asked Sep 25, 2014

25 votes

1 answer

2333

GATE CSE 1998 | Question: 2.7
The function represented by the Karnaugh map given below is $A.B$ $AB+BC+CA$ $\overline{B \oplus C}$ $A.BC$

The function represented by the Karnaugh map given below is$A.B$$AB+BC+CA$$\overline{B \oplus C}$$A.BC$

Kathleen

8.4k views

Kathleen asked Sep 25, 2014

31 votes

2 answers

2334

GATE CSE 1998 | Question: 1.17
The octal representation of an integer is $(342)_8$. If this were to be treated as an eight-bit integer in an $8085$ based computer, its decimal equivalent is $226$ $-98$ $76$ $-30$

The octal representation of an integer is $(342)_8$. If this were to be treated as an eight-bit integer in an $8085$ based computer, its decimal equivalent is$226$$-98$$7...

Kathleen

8.3k views

Kathleen asked Sep 25, 2014

1 votes

1 answer

2335

GATE CSE 1998 | Question: 1.15
The threshold level for logic 1 in the TTL family is any voltage above 2.5 V any voltage between 0.8 V and 5.0 V any voltage below 5.0 V any voltage below V$_{cc}$ but above 2.8 V

The threshold level for logic 1 in the TTL family isany voltage above 2.5 Vany voltage between 0.8 V and 5.0 Vany voltage below 5.0 Vany voltage below V$_{cc}$ but above ...

Kathleen

3.0k views

Kathleen asked Sep 25, 2014

24 votes

1 answer

2336

GATE CSE 1998 | Question: 1.14
A multiplexer with a $4-bit$ data select input is a $4:1$ multiplexer $2:1$ multiplexer $16:1$ multiplexer $8:1$ multiplexer

A multiplexer with a $4-bit$ data select input is a$4:1$ multiplexer$2:1$ multiplexer$16:1$ multiplexer$8:1$ multiplexer

Kathleen

9.2k views

Kathleen asked Sep 25, 2014

42 votes

4 answers

2337

GATE CSE 1998 | Question: 1.13
What happens when a bit-string is XORed with itself $n$-times as shown: $\left[B \oplus (B \oplus ( B \oplus (B \dots n \text{ times}\right]$ complements when $n$ is even complements when $n$ is odd divides by $2^n$ always remains unchanged when $n$ is even

What happens when a bit-string is XORed with itself $n$-times as shown:$\left[B \oplus (B \oplus ( B \oplus (B \dots n \text{ times}\right]$complements when $n$ is evenco...

Kathleen

10.2k views

Kathleen asked Sep 25, 2014

25 votes

5 answers

2338

GATE CSE 2012 | Question: 30
What is the minimal form of the Karnaugh map shown below? Assume that $X$ denotes a don’t care term $\bar{b} \bar{d}$ $ \bar { b } \bar { d } + \bar{b} \bar{c} $ $ \bar{b} \bar{d} + {a} \bar{b} \bar{c} {d}$ $ \bar{b} \bar{d} + \bar{b} \bar{c} + \bar{c} \bar{d} $

What is the minimal form of the Karnaugh map shown below? Assume that $X$ denotes a don’t care term $\bar{b} \bar{d}$$ \bar { b } \bar { d } + \bar{b} \bar{c} $$ \bar{b...

Arjun

6.5k views

Arjun asked Sep 25, 2014

32 votes

4 answers

2339

GATE CSE 2013 | Question: 46
A RAM chip has a capacity of 1024 words of 8 bits each (1K × 8). The number of 2 × 4 decoders with enable line needed to construct a 16K × 16 RAM from 1K × 8 RAM is (A) 4 (B) 5 (C) 6 (D) 7

A RAM chip has a capacity of 1024 words of 8 bits each (1K × 8). The number of 2 × 4 decoders with enable line needed to construct a 16K × 16 RAM from 1K × 8 RAM is(A...

Arjun

27.9k views

Arjun asked Sep 24, 2014

31 votes

7 answers

2340

GATE CSE 2013 | Question: 21
Which one of the following expressions does NOT represent exclusive NOR of $x$ and $y$? $xy + x′ y′$ $x\oplus y′$ $x′\oplus y$ $x′\oplus y′$

Which one of the following expressions does NOT represent exclusive NOR of $x$ and $y$?$xy + x′ y′$$x\oplus y′$$x′\oplus y$$x′\oplus y′$

Arjun

9.6k views

Arjun asked Sep 24, 2014

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