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

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

- C
- D
- A
**B**

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′

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)

Convert the binary number 1101 to decimal

- 12
**13**- 11
- 14
- 15

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

**Half-adder**- BCD Adder
- Adder-subtractor
- Full adder

What is the equivalent of 10110.01012 in hexadecimal number system?

- 26.2416
**16.516**- 18.2416
- 22.516

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**

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

**True**

What is the expression of this diagram?

- A` * Y * Z
- A` + Y + Z`
**A` + Y + Z**

Convert the binary number 10101100 to its decimal equivalent

**172**- 171
- 173
- 170
- 174

What kind of state machine is in the illustration below?

**A Mealy machine**

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

**0001,0010,0100,1000**

What is the answer to 1010 + 0101?

- 1011
**1111**- 0111
- 1001

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 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

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.

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

Convert the decimal number 65 to hexadecimal

- 43
- 42
- 40
**41**- 44

Which Boolean function best describes the logic diagram below?

- y=(a(bcd)′e)′
**y=((a(bcd)′e)′)′**- y=(abc′de′)′
- y=(a(bcd)e′)′

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

- POS
- SOP
- Maxterm
**Minterm**

It is a digital circuit that produces the arithmetic sum of

- Half-adder
**Binary adder**- BCD adder
- Full adder

Convert 111010010 from base 2 to base 8

**722**- 422
- 522
- 622

The output of (x+y′)′+(xz)

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

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

- Shift Registers
- Flip Flops
- Counters
**Multiplexers**

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

**False**

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

**Full adder**

Convert the decimal number 123 to binary equivalent

- 11110110
- 1111001
- 11111011
**1111011**- 1111010

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.

**Radix**- None of the above
- Name
- Unit

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

**Karnaugh map**

Find the two’s complement of the binary number 10001110

**01110010**

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

- True
**False**

_Select the Twos Compliment for -5

- 11111010
- 0000 0101
- 01111011
**11111011**

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

**True**- False

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**

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

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

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

**Subtraction**- Addition
- Division
- Multiplication

Convert 10011000 from base 2 to base 10

**152**- 153
- 252
- 253

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

- True
**False**

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

**Because we can always use resettable flip-flops.**

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

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

- x′y
- x
**xy**- x′

What is the objective of abstraction?

- Encrypting the data
**Hiding the complexity**- Simplifying the circuit
- Hiding the source code

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′)′

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

- Symbolic Logic
- Propositional Calculus
- Algebraic Function
**Binary Logic**

Find the two’s complement of the binary number 11011010

**00100110**

Convert the hexadecimal number AB to decimal:

- 172
- 170
**171**- 174
- 173

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

**Prime implicant**- Minterm
- Implicant
- Essential prime implicant

What is the equivalent of 3456

- 23310
- 13610
- 23410
**13710**

Which truth table is this? Exclusive-NOR Gate

- NOR
- OR
- XOR
**XNOR**

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

**ONE-HOT ENCODING**

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

**False**

In combinational circuits, output depends on

- Previous inputs
- Previous output
- Both a & b
**Present inputs**

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

**XOR**- OR
- XNOR
- NAND

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

- Sum
- Complement
**Product**- Identity

Add binary numbers shown?

- 01011010
- 10010101
- 10011010
**10100010**

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

_________ are the applications of flip flop

- Counters
- Storage devices
**All of the above**- Registers

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

- ABC
- A
- C
**B**

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

- NOR Gate
- NOT Gate
- AND Gate
**Ex-OR Gate**

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**

Find the four-bit sum of 1011+0101

**0000**

F(w,x,y,z)=Σ(2,4,7,10,12)

**x'z'+y'z'+w'xy**

Convert the hexadecimal number C3 to binary:

- 11100011
- 11000111
**11000011**- 11010011
- 11001011

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**

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

**BISTABLE**

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

- Ex-OR
- NOR
- OR
**NAND**

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**

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

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

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

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

- Algebraic functions
- Mathematical operators
**Logical operators**- Logical symbols

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

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

- Monostable state
- Bistable state
- Astable state
**Metastable state**

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

**0111,1011,1101,1110**

The output of the sequential circuit depends upon _________

- None of the above
- Past input
- Present input
**Present input and present state**

Obtain the simplified Boolean expression for the output F

**ABC+A'D**

Which truth table is this?

- NAND
- NOR
- AND
- OR
**NOT**

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

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**

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

**product of sums**

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

**State transition diagram**

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

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

Find the sum of 11001+(-11110).

**11011**

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′

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

- 110111
- 11110100
- 110101
**110100**

The clear input is used to make output ______

- Invalid
**Q=0**- Q=1
- No change

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'

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

**0**

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

- Invalid
- Set
**No change**- Reset

Convert 1011 from base 2 to base 8

**13**- 15
- 11
- 14
- 12

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

**Digital System**- Electronic System
- Binary System
- Information System

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

- Gregory Boole
- Gerard Boole
**George Boole**- Gregor Boole

What is the complement of xy′+x′y

**(x'+y)(x+y')**

Convert the binary number 10011 to hexadecimal

- 11
**13**- 14
- 15
- 12

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

**1**

Convert the binary number 11011011 to a decimal number

- 319
- 119
**219**- 519
- 419

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.**

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**

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`

Convert 4021.25

- 515.610
- 192.710
**511.410**- 822.610

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**

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.

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

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

**0**

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?

**[No Answer]**

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

**Moore machine**

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

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

**REGISTER**

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

- Indeterminate
- Set
**Reset**- No change

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

F(a,b,c,d)=Π(1,3,5,7,13,15)

- F=ac+b′d
**F=(a+d′)(b′+d′)**- F=ad′+bd′
- F=(a+c′)(b+d′)

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

- NOT operator
- NOR operator
- OR operator
**AND operator**

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

- Gray Code
**ASCII Code**- 2421
- BCD

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**

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

- R=1
**R=0**

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

- True
**False**

Convert 47 from base 16 to base 10

- 72
- 70
**71**- 73

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**

Convert 101111 from base 2 to base 16

- 1F
- 5F
- 3F
- 4F
**2F**

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

- 9
- 3
**16**- 12

Convert the hexadecimal number 230 to its binary equivalent

- 11000110000
- 10001110000
**1000110000**- 10001100000

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

**16**

1101

**4**

A flip flop is an __________

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

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**

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

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

**Maxterm**- POS
- Minterm
- SOP

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

**4**

Convert the decimal number 54 to binary:

**110110**- 110111
- 110100
- 111110

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

- J-K
- T
- S-R
**D**

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

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

**MEALY MACHINE**

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 circuit doesn’t have a memory unit?

- Sequential
- None of the above
- Both a and b
**Combinational**

Below are schematic diagrams of four circuits.

- (a), (b), and (c)
**(c) and (d)**- (a) and (b)
- (b), (c), and (d)
- (a) and (c)

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

- True
**False**

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**

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

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

**BINARY ENCODING**

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

- NOT
- AND
- OR
**NAND**

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)**

_Select the Two's Complement for -77

- 10110010
- 00110011
**10110011**

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