Logic Machines

Question 1

What type of input and output state do logic machines have?

Answer 1

binary input and output states: 0 and 1

Question 2

What is the relationship between input and output in an AND gate?

Answer 2

both inputs must be a 1 for the output to be 1. if either input is 0, the output will be 0.

Question 3

What is the boolean function for an AND gate, if x and y are inputs and z is the output?

Answer 3

z = x * y

Question 4

What is the relationship between input and output in an OR gate?

Answer 4

only one input must be a 1 for the output to be 1. the output can only be 0 if both inputs are 0.

Question 5

What is the boolean function for an OR gate, if x and y are inputs and z is the output?

Answer 5

z = x + y

Question 6

What is the relationship between input and output in a NOT gate?

Answer 6

the output is always the opposite state of the input

Question 7

What is the boolean function for a NOT gate, if x is the input and y is the output?

Answer 7

the opposite of x can be written as x’ or x̅, the boolean function would be y = x’, or y = x̅

Question 8

What are the two big examples of combined machines (gates)?

Answer 8

the NAND gate and the NOR gate

Question 9

What is the NAND gate?

Answer 9

an AND gate with an inverter (NOT gate) on the output

Question 10

What is the boolean function for a NAND gate, if x and y are the inputs and z is the output?

Answer 10

x̅ * y̅

Question 11

What is the NOR gate?

Answer 11

an OR gate with an inverter (NOT gate) on the output

Question 12

What is the boolean function for a NOR gate, if x and y are the inputs and z is the output?

Answer 12

x̅ + y̅

Question 13

What is the relationship between input and output in the Exclusive-OR gate?

Answer 13

the output value is 1 if and only if exactly one input is 1. if both inputs are 1 or both outputs are 0, then the output is 0.

Question 14

What is the Exclusive-NOR gate?

Answer 14

an Exclusive-OR gate with an inverter (NOT gate) on the output

Question 15

What is the Fredkin Gate?

Answer 15

A gate that takes in 3 outputs, A, B, and C, and produces 3 outputs X, Y, and Z.

Question 16

How does the Fredkin Gate work?

Answer 16

X is always the same as A. If A is 1, then the other two outputs are switched, i.e. Z = B and Y = C. Otherwise, if A is 0, the other two inputs pass through unchanged, i.e. Y = B and Z = C.

Question 17

What is unique about the NAND gate and the Fredkin Gate?

Answer 17

Any logical circuit can implemented using only NAND gates or only Fredkin gates.