Logic Gates

Question 1

What is a gate?

Answer 1

A device that performs a basic operation on electrical signals

Consist of transistors

Question 2

What are circuits?

Answer 2

Gates combined to perform more complicated tasks

Question 3

What are boolean expressions?

Answer 3

Uses Boolean algebra, a mathematical notation for expressing two-valued logic

Question 4

What are logic diagrams?

Answer 4

A graphical representation of a circuit; each gate has its own symbol

Question 5

What are truth tables?

Answer 5

A table showing all possible input values and the associated output values

Question 6

What is functional notation?

Answer 6

Uses a function name followed
by a list of arguments in place of
the operands used in Boolean
expressions

Question 7

What are the two main roles of transistors?

Answer 7

amplifier or binary switch

Question 8

What is a NOT gate? What are notations?

Answer 8

accepts one input signal (0 or 1) and returns the opposite signal as output, sometimes referred to as an inverter

X= A′= Ā= ¬A

Question 9

Why do we need to use transistors?

Answer 9

need to be able to implement the logic
functions in hardware and need to be able to pass the output
of one function to an input of another

they are power efficient and fast

Question 10

What is an AND gate? Notation?

Answer 10

accepts two signals (0 or 1)

returns a 1 if both signals are one, if not it returns a 0

X=A*B

Question 11

What is an OR gate? Notation?

Answer 11

accepts two signal (0 or 1)

returns a 0 if both inputs are zero otherwise it outputs a 1

X= A + B

Question 12

What is the NAND gate? Notation?

Answer 12

(NOT of AND gate)

accepts two input signals, if both are 1 the output is 0 otherwise the output is 1

X=(A*B)’

Question 13

What is the NOR gate? Notation?

Answer 13

(NOT of OR gate)

accepts two inputs, If both are 0, the output is 1; otherwise, the output is 0

X = (A+B)’

Question 14

Can some gates be generalized to accept three or more input values?

Answer 14

yes

Question 15

What would a three input AND gate act like?

Answer 15

will produce an output of 1 only if all input values are 1

Question 16

What is the XOR gate? Notation?

Answer 16

accepts only two input signals, if both inputs are the same the output is 0, otherwise it is 1

X= A (circle with cross) B

Question 17

What is the boolean and functional notation of NOT gate?

Answer 17

X=A’

X=NOT(A)

Question 18

What is the boolean and functional notation of OR gate?

Answer 18

X = A + B

X=OR(A,B)

Question 19

What is the boolean and functional notation of AND gate?

Answer 19

X = A * B

X=AND(A,B)

Question 20

What is the boolean and functional notation of NOR gate?

Answer 20

X = (A + B)’

X=NOT(OR(A,B))

Question 21

What is the boolean and functional notation of NAND gate?

Answer 21

X = (A * B)’

X=(NOT(AND(A,B))

Question 22

How can you define the XOR function in functional and boolean notation in terms of AND, OR, and NOT? How can the XOR function be simplified?

Answer 22

X = (A + B) * (A * B)’

X = AND(OR(A,B),NOT(AND(A,B)))

X = NOT(A=B)
X = A<>B

Question 23

How are circuits combined?

Answer 23

by using the output of one gate as the input for another

Question 24

How many rows in a truth table are required to show all outcomes for three inputs?

Answer 24

8

Question 25

What is the distributive law of boolean algebra?

Answer 25

you can turn X=AB + AC (3 gate circuit) into X=A * ( B + C) (2 gate circuit)

Question 26

How are addition operations carried out at the digital logic level?

Answer 26

special circuits called adders

Question 27

What is the difference between a half adder and a full adder?

Answer 27

half: computes the sum of two bits and produces the correct carry bit

full: computes the sum of two bits and a carry bit and produces the correct carry bit

Question 28

How many cases is evaluated to 1 in AND gate?

Answer 28

1 (input of 1,1)

Question 29

How many causes evaluate to 1 in XOR gate?

Answer 29

2 (1,0 and 0,1)

Question 30

What is a general formula to find the number of rows in a truth table given the number of inputs?

Answer 30

2^n

n is number of rows