Digital Systems ! - Units 3 & 4

What is the primary motivation for using Boolean algebra to simplify logic expressions?

-May make it easier to understand the circuit -May reduce the number of inputs required -May reduce the number of gates (Answer Choice: All of the Above)

Simplifying logic circuits results in:

-fewer connections -fewer potential faults -fewer gates (Answer choice: All of the Above)

Which of the following is a correct form of Boolean addition?

0 + 1 = 1

Which of the following is a correct form of Boolean multiplication?

0 · 1 = 0

A + 1 = ________.

1

The truth table for a three-input OR gate contains ________ entries.

8

A + 0 = ________.

A

Which of the following is not a reason for Boolean simplification?

A Boolean expression is longer.

Which of the examples below expresses the distributive law?

A(B + C) = AB + AC

Which of the examples below expresses the commutative law of multiplication?

AB = BA

Which logic function is represented by the equation AB = X?

AND

Which equation demonstrates the Distributive Law?

BA + CA = A(B + C)

Which equation demonstrates the Commutative Law?

C + AB = AB + C

Which of the following combinations cannot be combined into Karnaugh-map groups?

Diagonal corners

Which law of Boolean Algebra is applied in this equation? ABC + BC + A = BC(A + 1) + A

Distributive

Select the statement that best describes the use of Don't Care conditions on a K-map.

Don't Care conditions may be changed to either a 0 or a 1.

A combinatorial logic circuit has memory characteristics that remember the inputs after they have been removed.

False

Boolean multiplication is symbolized by A + B.

False

Single looping in groups of three is an allowable K-map simplification technique.

False

The commutative law of Boolean addition states that A + B = A · B.

False

The output of a NOR gate is LOW only when all inputs are HIGH.

False

The output of an AND gate is LOW only when all inputs are LOW.

False

When mapping an SOP expression using a Karnaugh map a 0 is placed in each cell corresponding to the value of the product term.

False

If one input of an AND gate is considered to be an enable, it will enable the other input when it is

HIGH.

Which statement below best describes a Karnaugh map?

Karnaugh maps provide a cookbook approach to simplifying Boolean expressions.

What will be the output of a three-input NOR gate whose inputs are a clock, a HIGH, and a LOW?

LOW

If input A of a NOR gate is LOW and input B is HIGH, the output should be

LOW.

If one input of an AND gate is LOW while the other is a clock signal, the output is

LOW.

The implementation of simplified sum-of-products expressions may be easily implemented into actual logic circuits using all ________ with little or no increase in circuit complexity.

NAND gates

An application requires a 3-input AND gate; however, all three of the inputs actually produce a LOW when the inputs are ON. What type of logic gate would lend itself to this application?

NOR

Which of the following gates generates the exact inverse output of the OR gate for all possible input combinations?

NOR

The logic gate that generates a HIGH (1) output only when all of its inputs are LOW (0) is the:

NOR gate

The basic logic circuit whose output equals the Boolean algebraic sum of its input is the:

OR gate.

The logic gate that generates a HIGH (1) output when any one of its inputs is HIGH is the:

OR gate.

Table 4-1 L M N Z 0 0 0 0 0 0 1 0 0 1 0 1 0 1 1 0 1 0 0 1 1 0 1 0 1 1 0 1 1 1 1 0 The truth table in Table 4-1 indicates that:

The output (Z) is HIGH only when the binary input count is an even number greater than zero.

An AND gate is checked for operation and the following readings are taken on the gate: input A = 0.2V, input B = 4.5V, input C = 0.4V, output = 4.9V. What might be wrong with the gate?

The output is stuck high; the chip is bad.

A square in the top row of a K-map is considered to be adjacent to its corresponding square in the bottom row.

True

Generally speaking, when AND and OR gates are used to enable signals, the output signal will follow the desired input signal exactly.

True

In Boolean algebra, 1 · 0 = 0.

True

In true sum-of-products expressions an inversion bar cannot cover more than single variables in a term.

True

One characteristic of an Exclusive-OR gate is that it can be used as a controlled inverter.

True

One method of determining an output from a logic circuit is to simply track the inputs through the gates and determine the output.

True

The Boolean expression for a three-input AND gate is X = ABC.

True

The Sum-of-Product (SOP) form is a standard form of a Boolean expression.

True

The complement of 1 is 0.

True

When the inputs to a 3-input NAND gate are 001, the output is 1.

True

When the inputs to a 3-input OR gate are 001, the output is 1.

True

Table 4-1 L M N Z 0 0 0 0 0 0 1 0 0 1 0 1 0 1 1 0 1 0 0 1 1 0 1 0 1 1 0 1 1 1 1 0 Circuit implementation of the simplified expression for Table 4-1 will require (as a minimum):

Two 2-input AND gates, one 2-input OR gate, and one inverter.

Which of the following is the simplest form of the expression Y = ABC[AB + C(BC + AC)]?

V = ABC

The simplest form of X = A(B + C) + AC is ________.

X = AB + AC

Which answer is an example of a sum-of-products (SOP) expression?

X = AB + AC

Using Boolean algebra to simplify the expression Z = AB + A(B + C) + B(B + C), the completed first step would result in the expression:

Z = AB + AB + AC + BB + BC

An OR gate with inverted inputs functions as

a NAND gate.

The final output of a product-of-sum (POS) circuit is generated by

an AND.

X(YZ) = (XY)Z is an example of the

associative law.

AB + AC = A(B + C) is an example of the

distributive law.

Occasionally, a particular logic expression will be of no consequence in the operation of a circuit, such as in a BCD-to-decimal converter. These result in ________ terms in the K-map and can be treated as either ________ or ________, in order to ________ the resulting term.

don't care; 1's; 0's; simplify

How many two-input gates are in a single 14-pin DIP integrated circuit?

four

If both inputs of an AND gate are normally HIGH but one of them momentarily dips LOW, the output will

momentarily dip LOW

A three-input NAND gate will have a HIGH output whenever

one input is LOW.

A Karnaugh map ________.

produces the simplest sum-of-products expression

How many inverters are in a 14-pin DIP integrated circuit?

six

If both inputs of an OR gate are normally HIGH but one of them momentarily dips LOW, the output will

stay HIGH.

DeMorgan's Theorem is used to simplify circuits

that contain NORs and NANDs.

How many two-input gates are needed to build the logic circuit represented by X = C(A+B)?

two

A NAND gate with one HIGH input and one LOW input

will output a HIGH

When ones in a Karnaugh Map are not next to each other visually, they can be grouped if they are next to each other by means of

wraparound.