Logic Gates and Circuits

Question 1

x + x and x * x is equal to? Also what is the rule called?

Answer 1

x + x = x, x* x = x (Idenpotent Rule)

Question 2

What is the rule, where anything + 1 is equal to 1?

Answer 2

x + 1 = 1 , Unit and Zero property

Question 3

What is the zero property with products (AND GATES)?

Answer 3

x*0 = 0

Question 4

What is the fancy word for double negation?

Answer 4

Involution x = ((x)’)’

Question 5

What does the associative rule mean? Does it work for both OR and AND gates?

Answer 5

Yes!
x + ( y + z) = (x + y) + z
x · (y · z) = (x ·y) · z

Question 6

What is Demorgan’s law.

Answer 6

(x+y)' = x'y'
(xy)' = x' + y'

Question 7

What is the absorption law?

Answer 7

x + xy = x

x · (x + y) = x

Question 8

What is the operator precedance?

Answer 8

1- Brackets
2- NOT
3- AND
4- OR

Question 9

What are the common ways to minimize logic circuit?

Answer 9

By using boolean algebra and/or K-maps

Question 10

What are Minterms and Maxterms?

Answer 10

minterms are when the function’s output is 1 (true). The max term is when the function’s output is 0.

Question 11

How is the k-map setup?

Answer 11

the k-map must be setup so that only 1 variable changes from one box to the other.
Ex: 00, 01, 11, 10

Question 12

What are the restrictions of the k-map?

Answer 12

The k-map can only use 4 or 5 variables.

Question 13

What is a prime implicant?

Answer 13

The prime implicant is the most reduced expression.

Question 14

What is the difference between SOP and POS.

Answer 14

Sum of products. Example: ABC+A’B+B’C

Product of sums Example: (A+B+C)(A’+B)(B’+C)

Question 15

How do you simplify using the K-map?

Answer 15

By making groups of 2^n
Groups of 2 -> 1 variable gets dropped
Groups of 4 ->2 variables gets dropped
Group of 8 -> 3 variables gets dropped

Question 16

Why do people tend to design their circuits using NAND gates?

Answer 16

Because the NAND gates are cheaper to build and they make the circuit easier to physically implement.

Question 17

How do you deal with extra inputs to a AND logic gate?

Answer 17

By connecting the left over inputs to 1.

Question 18

How do you deal with extra inputs to a OR logic gate?

Answer 18

By connecting the left over inputs to 0.

Question 19

How do you implement an AND gate using only NAND?

Answer 19

By using only 2 NAND gates.
Results (gate by gate)
AB->(AB)’->((AB)’)’ -> AB

Question 20

How do you implement a NOT gate using NAND?

Answer 20

By connecting the same variable to both inputs of the NAND. since, (AA)’ = A’

Question 21

How do you implement a NOR gate using NAND gates?

Answer 21

By using 3 NAND gates. Using the same principale as the NOT gate, You can get A going into the 2 inputs of the first NAND gate exclusively. You can also do that with B. That way you have A’ and B’ as inputs into the last NAND gate. Which result in (A’B’)’ = A+B

Question 22

What is the boolean expression for XOR gate?

Answer 22

F = A’B + AB’