Logic Gates and Gate Combinations

Question 1

What does an AND ( D- ) gate do and what is it performed by?

Answer 1

Produces a high output if all inputs are high, performed by a circuit called AND gate

Question 2

What does an OR gate do and what is it performed by?

Answer 2

Produces a high input if one or more inputs are high, performed by a circuit called OR gate

Question 3

What does a NOT ( -I>o- ) gate do and what is it performed by?

Answer 3

Changes one logic level to the other logic level, performed by a circuit called inverter

Question 4

What does the comparison function do?

Answer 4

The comparison function indicates whether a binary value is greater than, equal to, or less than, another

Question 5

What does the arithmetic function include?

Answer 5

Addition, subtraction, multiplication, and division

Question 6

What is a encoder?

Answer 6

A circuit that converts information into a coded
form

Question 7

What is a multiplexer?

Answer 7

A circuit that connects one of several data inputs to a
single data output line; also called a mux

A demultiplexer does the opposite

Question 8

What is a counter?

Answer 8

A sequential device; a state machine that has a
unique internal sequence of states. Counters are used to count events or to generate output sequences represented by changing levels or pulses

Question 9

Define programmable logic?

Answer 9

A category of digital integrated circuits capable of
being programmed to perform specified functions

Question 10

What are programmable logic devices (PLDs)?

Answer 10

Programmable logic devices (PLDs) are an alternative to fixed function devices. The logic can be programmed for a specific purpose. In general, they cost less and use less board space that fixed function devices

Question 11

What is a variable and value could it have?

Answer 11

A variable is a symbol used to represent an action, a condition, or data. Each variable has a value of 1 or 0

Question 12

What is the complement?

Answer 12

The complement represents the inverse of a variable; indicated by an over-bar.

Question 13

What is a literal?

Answer 13

A literal is a variable or its complement

Question 14

What does Addition(+) mean in Boolean algebra?

Answer 14

• Addition is equivalent to the OR operation
• The sum term is 1 if one or more if the literals are 1
• The sum term is zero only if each literal is 0

Question 15

What does Multiplication(.) mean in Boolean algebra?

Answer 15

• Multiplication is equivalent to the AND
  operation
• The product term (AND gate output) equals 1 only when each literal equals 1

Question 16

What does the commutative law state for addition?

Answer 16

In terms of the result, the order in which variables are ORed makes no difference
A + B = B + A

Question 17

What does the commutative law state for multiplication?

Answer 17

In terms of the result, the order in which variables are ANDed makes no difference
AB = BA

Question 18

For addition, the associative law states?

Answer 18

When ORing more than two variables, the result is the same regardless of the grouping of the variables
A + (B +C) = (A + B) + C

Question 19

For multiplication, the associative law states?

Answer 19

When ANDing more than two variables, the result is the same regardless of the grouping of the variables
A(BC) = (AB)C

Question 20

What is the distributive law?

Answer 20

• The distributive law is the factoring law
• A common variable can be factored from an expression just as in ordinary algebra
  AB + AC = A(B+ C)

Question 21

Explain why A + 0 = A

Answer 21

• When A = 1, the input causes the output to go to X = 1.
• When A = 0, the 0 inputs cause the output to go to X = 0.
• In either case, the value of X equals the value of A

Question 22

Explain why A + 1 = 1

Answer 22

• When A = 1, the inputs cause the output to go to X = 1.
• When A = 0, the 1 input caused the output to go to X = 1.
• In either case, the value of X equals one (1)

Question 23

Explain why A . 0 = 0

Answer 23

• When either input to an AND gate equals 0, the output from the gate has a value of X = 0, regardless of the value at the other input

Question 24

Explain why A . 1 = A

Answer 24

• When one input to an AND gate equals 1, the output from the gate has a value of X = A. - As shown, X = 1 when A = 1 and
  X = 0 when A = 0

Question 25

Explain why A + A = A

Answer 25

• When the inputs to an OR gate are equal, the output equals the value at the inputs
• When both inputs equal 1, the gate output is X = 1
• When both inputs equal 0, the gate output is X = 0

Question 26

Explain why
__
A + A = 1

Answer 26

When the inputs to an OR gate are unequal, one of the two always equals 1
- When either input equals 1, the gate output is X = 1
- Therefore, the output from the OR
gate equals 1 whenever the inputs are unequal (complementary)

Question 27

Explain why A . A = A

Answer 27

When the inputs to an AND gate are equal, the gate output also equals that value. Thus, X = 1 when both inputs equal 1 and X = 0 when both inputs equal 0

Question 28

Explain why
__
A . A = 0

Answer 28

When the inputs to an AND gate are unequal, one of the two always equals 0. When either input equals 0, the gate output is X = 0. Therefore, the output from the AND gate equals 0 whenever the inputs are unequal

Question 29

Explain why

A = A

Answer 29

When a value is inverted, it is the complement of the
original value. When inverted a second time, it
returns to its original value

Question 30

Explain why A + AB = A

Answer 30

When you use a truth table to represent this data for every possible combination of A and B. In each case, the output from the OR gate equals the value of A. Thus, A + AB always equals the value of A

Question 31

Explain why
__
A + AB = A + B

Answer 31

A truth table showing the outputs from the two circuits would show that for every possible combination of A and B, the two functions (A + AB) and (A + B) are equal

Question 32

Explain why (A + B)(A + C) = A + BC

Answer 32

If you split these into two circuits, the outputs from the two circuits using a truth table will be equal

Question 33

What is an inverter?

Answer 33

• A logic circuit that inverts or complements its
  inputs, it performs the NOT operation
• The NOT operation (complement) is shown with an overbar

Question 34

What is a timing diagram?

Answer 34

A diagram of waveforms showing the proper
time relationship of all of the waveforms

Question 35

What is a NAND gate?

Answer 35

A logic gate that produces a LOW output only
when all of its inputs are HIGH
_____
X = A . B

Question 36

What is NOR gate?

Answer 36

A logic gate that produces a LOW output when
one or more inputs are HIGH
______
X = A + B

Question 37

What is a Exclusive-OR gate (XOR)?

Answer 37

A logic gate that produces a HIGH output only
when its two inputs are at opposite levels
_ _
X = AB + AB

Question 38

What is a Exclusive-NOR gate (XNOR)?

Answer 38

A logic gate that produces a LOW output only
when its two inputs are at opposite levels
_ _
X = AB + AB