Logic Gates And Boolean Algebra

Question 1

What is the order of logic gates simplification?

Answer 1

• Brackets
• Negation (NOT)
• Multiplication (AND)
• Addition (OR)

Question 2

What are the commutative laws?

Answer 2

• A /\ B = B /\ A

- A V B = B V A

Question 3

What are the associative laws?

Answer 3

• (A V B) V C = A V (B V C) = A V B V C

- (A /\ B) /\ C = A /\ (B /\ C) = A /\ B /\ C

Question 4

What are the distributive laws?

Answer 4

• A /\ (B V C) = (A /\ B) V (A /\ C)

- A V B /\ C = (A V B) /\ (A V C)

Question 5

What are De Morgan’s Laws?

Answer 5

¬(A V B) = ¬A /\ ¬B

¬(A /\ B) = ¬A V ¬B

Question 6

What are the AND rules?

Answer 6

• A /\ 0 = 0
• A /\ A = A
• A /\ 1 = A
• A /\ ¬A = 0

Question 7

What are the OR rules?

Answer 7

• A V 0 = A
• A V 1 = 1
• A V A = A
• A V ¬A = 1

Question 8

Why do we simplify boolean algebra?

Answer 8

• practical use in circuit design

- fewer gates = cheaper

Question 9

What is a NAND gate? Truth table?

Answer 9

• table in book
• AND combined with a NOT gate
• true all the time unless both inputs are true

Question 10

What is a NOR gate? Truth table?

Answer 10

• table in book
• NOT and OR gate combined
• only true if both inputs are false

Question 11

What is a XOR gate? Truth table?

Answer 11

• exclusive OR

- true if one of the inputs is but not if both are

Question 12

What are adder circuits used for?

Answer 12

Binary addition - also deals with carry digits

Question 13

What is a half adder?

Answer 13

• 2 inputs and a carry digit are fed to it

- carry digit and an output are generated

Question 14

What is a full adder?

Answer 14

• 2 inputs and a carry and sent in
• sum of 2 inputs is sent to another adder and combined with original carry digit to create the final sum.
• Carry digit of first sum is sent to a OR gate and combined with carry digit of second sum to produce final carry digit output

Question 15

What is a flip-flop circuit?

Answer 15

• circuit compromising of NAND dates (storage used in SSD’s)
• can exist in either on or off state which enables it to store store one item of data (1 or 0). Flips between the 2 states, hence name
• combine to make other range of flip flops

Question 16

What is the D-type flip flop?

Answer 16

• combination of 2 flip-flops
• uses clock controlled circuit to control the output, delaying it by on clock pulse. D stands for delay
• 2 inputs; data and clock; and two outputs: they delayed data and the inverse of the delayed data

Question 17

Draw a flip-flop and D type flip-flop circuit

Answer 17

Images in book