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# Logic Circuit and Switching Theory

Uses switches to understand the operation of doors and digital logical circuits and contribute to the development of better theoretical knowledge.

## encoders

Find the two’s complement of the binary number 10001110

• 01110010

It states that every algebraic expression that we can logically construct from the postulates of Boolean algebra are valid even when the operators and identity elements interchange.

• Duality Principle
• DeMorgan’s Theorem
• Associative Theorem
• Commutative Postulate

In K-map, which of the following order sequence is correct for the input values representation?

• (00, 01, 10, 11)
• (00, 01, 11, 10)
• (00, 10, 11, 01)
• (00, 10, 01, 11)

1101

• 4

What is the expression of this diagram?

• A` * Y * Z
• A` + Y + Z`
• A` + Y + Z

Which of the following best represents the sum of minterms form of the function f=bd′+acd′+ab′c+a′c′?

• f(a,b,c,d)=∑(0,1,4,5,6,10,11,12,14)

if A = 1, B = 1, C = 0, D = B

• 0

What is the expression in this diagram?

• (A + Y)* Z
• A * Y* Z
• (A + Y)* Z`

In the state transition diagram below, the arc labeled Reset indicates that the system is going to:

• Reset upon entering the state.
• TA=TRUE
• Enter the state upon reset.
• TA=FALSE

An elevator can be at one of two floors: GROUND (0), or FIRST (1). There is one button that controls the elevator and it has two values: UP (1) or DOWN (0). There are also two lights in the elevator that indicate the floor: RED for Ground, and GREEN for First (Light OFF = 0; Light ON = 1). At each clock cycle, the controller checks the current floor and current input, changes floors and lights in the obvious way. Which of the following is the corresponding FSM diagram of this system?

Why is it no longer necessary to include Reset in the state transition table?

• Because we can always use resettable flip-flops.

We combine adjacent squares of the K-map that contain zeros to obtain which simplified form of Boolean function?

• product of sums

Convert the Boolean function described by F(x,y)=∑(1,2,3) to the other canonical form.

• F = x'y+xy'
• F = x+y
• F = x+y'
• F = xy+x'y'

Which is true about the cross-coupled NOR gates below?

• R=1
• R=0

Which truth table is this?

• NAND
• NOR
• AND
• OR
• NOT

It is a finite state machine whose output depends on both current state and current inputs of the machine.

• MEALY MACHINE

_________ are the applications of flip flop

• Counters
• Storage devices
• All of the above
• Registers

He is an English mathematician after whom Boolean algebra was named.

• Gregory Boole
• Gerard Boole
• George Boole
• Gregor Boole

TRUE OR FALSE: Race condition only happens with asynchronous circuits, never with synchronous circuits or combinational circuits.

• True
• False

What is the equivalent one-hot encoding of a finite state machine with four states?

• 0001,0010,0100,1000

It is a finite state machine whose output depends only on the current state of the machine.

• Moore machine

Binary logic consists of binary variables and a set of ____________________.

• Algebraic functions
• Mathematical operators
• Logical operators
• Logical symbols

The clear input is used to make output ______

• Invalid
• Q=0
• Q=1
• No change

Why would you build a BCD-to-binary converter circuit?

• Different parts of the system may use different binary codes.
• Only humans can comprehend BCD.
• None of the above.
• The converter will translate all binary numbers into BCD.

This occurs only when adding numbers in two's complement system that have the same sign, and whose result appears to be in the opposite sign.

• Sign flag = 1
• Signed overflow
• Unsigned overflow
• Carry flag = 0

The output of the sequential circuit depends upon _________

• None of the above
• Past input
• Present input
• Present input and present state

TRUE OR FALSE: A latch is said to be opaque when it allows the data to flow through to the output.

• True
• False

TRUE OR FALSE: Finite state machines provide a systematic way to design combinational circuits, given a functional specification.

• True
• False

• 01011010
• 10010101
• 10011010
• 10100010

It deals with variables that take on two discrete values, and operations that assume logical meaning.

• Symbolic Logic
• Propositional Calculus
• Algebraic Function
• Binary Logic

What is the answer to 1010 + 0101?

• 1011
• 1111
• 0111
• 1001

Reduce the Boolean expression, A'B(D'+C'D)+B(A+A'CD), to one literal.

• C
• D
• A
• B

The ______ of a number system gives the number of symbols used in a system; it is always expressed in decimal numbers and is indicated by a subscript.

• None of the above
• Name
• Unit

_Select the Twos Compliment for -5

• 11111010
• 0000 0101
• 01111011
• 11111011

It is a Boolean term composed of one or more literals joined by the AND operation.

• Sum
• Complement
• Product
• Identity

Obtain the simplified Boolean expression for the output F

• ABC+A'D

F(w,x,y,z)=Σ(2,4,7,10,12)

• x'z'+y'z'+w'xy

Refer to the circuit diagram below. Assume that initially Q=1 and Q′=0, and CLK=0. What would be the value of Q and Q′ if we set CLK=1 and D=1?

• Q=1,Q′=1
• Q=1,Q′=0
• Q=0,Q′=1
• Q=0,Q′=0

Convert 10011000 from base 2 to base 10

• 152
• 153
• 252
• 253

Convert the decimal number 54 to binary:

• 110110
• 110111
• 110100
• 111110

It is a set of state variables that contain all the information about the past necessary to explain the future behavior of a circuit.

• State of the system

The following are steps involved in designing combinational circuits, except one:

• Label the inputs and outputs with arbitrary symbols.
• Obtain the simplified Boolean functions of the output in terms of the input.
• Draw the diagram.
• Derive the truth table.

Convert the hexadecimal number C3 to binary:

• 11100011
• 11000111
• 11000011
• 11010011
• 11001011

This operator is typically represented by the absence of an operator.

• NOT operator
• NOR operator
• OR operator
• AND operator

_Select the Two's Complement for -77

• 10110010
• 00110011
• 10110011

TRUE OR FALSE: In the state transition diagrams of Moore machines, outputs are labeled in the circles.

• True

Finding the complements of numbers simplifies which operation in digital systems?

• Subtraction
• Division
• Multiplication

The 8-bit sum of the signed numbers (-23) and (+11) in two’s complement form is _________.

• 1111 0100
• 1111 1000
• 1111 1100
• 1111 1101

if A=1, B=0, C=1, and D=0. Refer to the figure below:

• 0

The following are equivalent functions of F(A,B,C,D)=Σ(0,6,8,13,14) with don't-care conditions d(A,B,C,D)=Σ(2,4,10), except one.

• F=(B+D)′+(C′+D)′+(A+D)′+(A′+B′+C+D′)′
• F=B′D′+CD′+A′D′+ABC′D
• F=D⊕ABC′
• F=(D⊕ABC′)′

What is the equivalent of 10110.01012 in hexadecimal number system?

• 26.2416
• 16.516
• 18.2416
• 22.516

How would a negative edge-triggered (D) flip-flop behave? Select all that apply.

• The flip-flop will copy D to Q on the rising edge of the clock
• The flip-flop will retain its state on the falling edge of the clock.
• The flip-flop will copy D to Q on the falling edge of the clock.
• The flip-flop will retain its state on the rising edge of the clock.

Convert the binary number 1101 to decimal

• 12
• 13
• 11
• 14
• 15

In combinational circuits, output depends on

• Previous inputs
• Previous output
• Both a & b
• Present inputs

You are designing an FSM to keep track of the mood of four students working in the digital design lab. Each student's mood is either HAPPY, SAD, BUSY, CLUELESS, or ASLEEP. You have factored the FSM into four multiple simple machines, one for each student. What is the minimum total number of bits necessary in this factored design?

• 12

It is part of mathematics that deals with operations involving logical elements, variables and operators, axioms and postulates.

• Propositional Calculus
• Fuzzy Logic
• Boolean Algebra
• Symbolic Logic

What is the equivalent one-cold encoding of a finite state machine with four states?

• 0111,1011,1101,1110

Convert 47 from base 16 to base 10

• 72
• 70
• 71
• 73

You are designing an FSM to keep track of the mood of four students working in the digital design lab. Each student's mood is either HAPPY, SAD, BUSY, CLUELESS, or ASLEEP. What is the minimum number of bits necessary to represent the FSM's states?

• 5

Convert 1011 from base 2 to base 8

• 13
• 15
• 11
• 14
• 12

TRUE OR FALSE: The number of adjacent squares that can be combined in a K-map must be a multiple of 2.

• True
• False

We use _______________ to find the decimal equivalent of a particular value expressed in a different number system.

• Positional notation
• Interval notation
• Scientific notation
• Set builder notation

This type of encoding uses a separate bit for each state; only one bit is true at any time.

• ONE-HOT ENCODING

Convert the decimal number 123 to binary equivalent

• 11110110
• 1111001
• 11111011
• 1111011
• 1111010

TRUE OR FALSE: When adding positive numbers in two's complement system, there is no signed overflow when neither a carry into nor a carry out of the sign bit occurs.

• True
• False

Convert the binary number 11011011 to a decimal number

• 319
• 119
• 219
• 519
• 419

It is a combinational circuit that performs addition of two bits.

The simplified form of the Boolean expression, x(x′+y)

• x′y
• x
• xy
• x′

The logic gate for which output is equal to 1 only when both the inputs are 1

• NAND gate
• AND gate
• OR gate
• NOT gate

It is a graphical representation of the possible states of the system and the transitions between these states.

• State transition diagram

In which flip flop the present input will be the next output?

• J-K
• T
• S-R
• D

The output of (x+y′)′+(xz)

• None of the above
• 1 and 0
• 1
• 0
• xy′+x′z′

if A=1, B=0, C=0, D=1. Refer to the figure below.

• 1

Find the four-bit sum of 1011+0101

• 0000

It is a product term obtained by combining the maximum possible number of adjacent squares.

• Prime implicant
• Minterm
• Implicant
• Essential prime implicant

This latch is one of the simplest circuits--composed of cross-coupled NOR gates--whose state can be controlled through its set and reset inputs.

• SR LATCH

What is the complement of xy′+x′y

• (x'+y)(x+y')

You are designing an elevator controller for a building with 25 floors. The controller has two inputs, UP and DOWN. It produces an output indicating the floor that the elevator is on. There is no Floor 13. What is the minimum number of bits of state in the controller?

• 5

FFFFF Alyssa's snail (see Module 11) has a daughter with a Machine FSM brain. The daughter snail smiles whenever she slides over the pattern 1101 or the pattern 1110. What is the minimum number of states for this happy snail?

• 4

Which Boolean function best describes the logic diagram below?

• y=(a(bcd)′e)′
• y=((a(bcd)′e)′)′
• y=(abc′de′)′
• y=(a(bcd)e′)′

Which of the following is the best example of a combinational logic circuit?

• Shift Registers
• Flip Flops
• Counters
• Multiplexers

Which of the following gate is one of the universal gates?

• NOT
• AND
• OR
• NAND

Find the sum of 11001+(-11110).

• 11011

Convert the binary number 10011 to hexadecimal

• 11
• 13
• 14
• 15
• 12

When an inverter is connected to the AND gate’s output then what logic function can be generated?

• Ex-OR
• NOR
• OR
• NAND

If a logic gate includes 4 inputs then how many possible combinations can be performed?

• 9
• 3
• 16
• 12

F(a,b,c,d)=Π(1,3,5,7,13,15)

• F=ac+b′d
• F=(a+d′)(b′+d′)
• F=(a+c′)(b+d′)

How many Boolean functions can we construct with two input variables involved?

• 16

What is the standard form of S-R flip flop?

• None of the above
• Single-Reset
• Simple-Reset
• Set Reset

What is the objective of abstraction?

• Encrypting the data
• Hiding the complexity
• Simplifying the circuit
• Hiding the source code

Below are schematic diagrams of four circuits.

• (a), (b), and (c)
• (c) and (d)
• (a) and (b)
• (b), (c), and (d)
• (a) and (c)

When the set is disabled and reset is enabled in S-R flip flop then the output will be __________

• Indeterminate
• Set
• Reset
• No change

It is a sequential circuit whose element is either a register or a combined circuit and has a clock input that is received by all registers in the circuit.

• SYNCHRONOUS SEQUENTIAL CIRCUIT

Which of the following is the simplified Sum of Products equivalent of the Boolean function F(w,x,y,z)=Π(1,3,5,7,13,15)

• F=wy′+xz
• F=wz′+x′z′
• F=z′+wx′
• F=w′z′+xz′

When the set is enabled in S-R flip flop then the output will be

• Indeterminate
• No change
• Set
• Reset

You are designing an FSM to keep track of the mood of four students working in the digital design lab. Each student's mood is either HAPPY, SAD, BUSY, CLUELESS, or ASLEEP. You have factored the FSM into four multiple simple machines, one for each student. How many states does each simpler machine have?

• 5

In some finite state machine diagrams (particularly Deterministic Finite Machine), there are states called accepting states, which are states that either accept or reject the previous input sequence. They either output TRUE or FALSE. Accepting states are represented in diagrams by a circle inside another circle. The finite state machine below generates a string of letters: Which of the following cannot be valid strings generated by the FSM?

• aaaaaacd

Which of the following logic gate is used to test odd parity?

• NOR Gate
• NOT Gate
• AND Gate
• Ex-OR Gate

Which truth table is this? XOR Gate & XNOR Gate: Truth Table, Symbol & Boolean Expression | Electrical4U

• XOR
• OR
• XNOR
• NAND

TRUE OR FALSE: A one-cold encoding is an encoding in which K states are represented with K bits, one of which is FALSE.

• True
• False

These are combinational circuits that perform the addition of three bits.

Convert 111010010 from base 2 to base 8

• 722
• 422
• 522
• 622

It is a third state which hovers between high and low states.

• Monostable state
• Bistable state
• Astable state
• Metastable state

What is the equivalent of 3456

• 23310
• 13610
• 23410
• 13710

Convert the hexadecimal number AB to decimal:

• 172
• 170
• 171
• 174
• 173

The state transition diagram of a state machine is given below.

• Q=S1
• S′0=S¯1S¯0A
• S′1=S0B
• S′1=S0A
• S′0=S¯1S¯0B
• Q=S¯1B

Convert the binary number 10101100 to its decimal equivalent

• 172
• 171
• 173
• 170
• 174

Which of the following logic gates are used to build a half adder ?

• AND & OR
• AND & EX-OR
• OR & NAND gate
• EX-OR & AND

TRUE OR FALSE: Next state equations can be simplified by Karnaugh maps.

• True
• False

What kind of state machine is in the illustration below?

• A Mealy machine

It is a product term involving all inputs of the function.

• POS
• SOP
• Maxterm
• Minterm

It is a system that manipulates discrete elements of information represented internally in binary form.

• Digital System
• Electronic System
• Binary System
• Information System

Convert the Boolean function described by F(x,y)=∑(1,2,3)

• F=xy+x′y′
• F=x+y
• F=x′+y′
• F=x′y+xy′
• F=x+y′

TRUE OR FALSE: A D flip-flop copies D to Q on the rising edge of the clock and remembers its state at all other times.

• true

Convert 4021.25

• 515.610
• 192.710
• 511.410
• 822.610

It is a bank of flip-flops that share a common clock input.

• REGISTER

TRUE OR FALSE: When adding negative numbers in two's complement system, signed overflow occurs when there is a carry into and a carry out of the sign bit.

• True
• False

Obtain the simplified Boolean expression for the output G in terms of the input variables in the circuit shown below. Give the expression only (no need to include G=), and do not put spaces between the variables and operators.

• A'D'+ABC

This latch has two inputs: a data input that controls what the next state should be, and a clock input which controls when the state should change.

• D LATCH

Which circuit doesn’t have a memory unit?

• Sequential
• None of the above
• Both a and b
• Combinational

1 0 0 0 1 1 1 - 1 0 0 1 1

• 110111
• 11110100
• 110101
• 110100

Convert 101111 from base 2 to base 16

• 1F
• 5F
• 3F
• 4F
• 2F

When S=0, R=0, CLK=X then the output will be ___________

• Invalid
• Set
• No change
• Reset

It is a table or diagram made up of squares which provides a simple way to minimize Boolean functions.

• Karnaugh map

It is a logic circuit consisting of gates whose outputs at any time are a function of the combination of inputs.

• Serial logic circuit
• Sequential logic circuit
• Parallel logic circuit
• Combinational logic circuit
• F=w′z′+xz′

It is a sum term involving all inputs of the function.

• Maxterm
• POS
• Minterm
• SOP

These are electronic circuits that operate on one or more input signals to produce an output signal.

• Amplifier circuits
• Logic gates
• Integrated circuits
• RLC circuits

Find the two’s complement of the binary number 11011010

• 00100110

TRUE OR FALSE: When both S¯ and R¯ in the circuit below are asserted, the circuit drives both outputs to 0.

• False

In choosing an FSM design style, the timing of the output response does not need to be considered.

• False

It is a digital circuit that produces the arithmetic sum of

This type of encoding represents each state as a binary number.

• BINARY ENCODING

Which truth table is this? Exclusive-NOR Gate

• NOR
• OR
• XOR
• XNOR

TRUE OR FALSE: In relation to FSMs, a state is a description of the status of a system that is waiting to execute a transition.

• True
• False

In a four-variable K-Map, how many adjacent squares will produce a product term with 2 literals?

• 4

An element with two stable states is called a __ element.

• BISTABLE

A flip flop is an __________

• Edge sensitive device
• Both a and b
• Synchronous device
• None of the above

This is a term in a Boolean expression that is redundant and can be eliminated so that a simpler expression can be obtained.

• Complement term
• Minterm
• Consensus term
• Maxterm

Convert the hexadecimal number 230 to its binary equivalent

• 11000110000
• 10001110000
• 1000110000
• 10001100000

if A=0, B=1, C=0 and D=A

• 0

It is a logic circuit composed of logic gates and storage elements. Its output is a function of the inputs and the state of the storage elements.

• Serial logic circuit
• Combinational logic circuit
• Sequential logic circuit
• Parallel logic circuit

Which of the following is a self-complementing binary code?

• Gray Code
• ASCII Code
• 2421
• BCD

The code in which each decimal digit is replaced by a combination of four binary digits is

• All of these
• Excess-3
• BCD
• Grey code

Convert the decimal number 65 to hexadecimal

• 43
• 42
• 40
• 41
• 44

The simplified form of the Boolean expression, ABC+A′B+ABC

• ABC
• A
• C
• B

Juan T. Masipag's company would like to design an FSM that takes two inputs, A and B, and generates one output, Z. The output in clock cycle n, denoted by Zn is either the Boolean AND or OR of the corresponding input An and the previous input An−1, depending on the other input Bn:

• A Mealy machine