Boolean logic

Question 1

What is the difference between boolean logic and boolean algebra?

Answer 1

• Boolean logic refers to the principles of logic based on binary values
• Boolean algebra is a mathematical system used to manipulate boolean values

Question 2

Boolean notation for AND

Answer 2

A ∧ B
A . B

Question 3

Boolean notation for OR

Answer 3

A V B
A + B

Question 4

Boolean notation for NOT

Answer 4

¬A

Question 5

Boolean notaiton for XOR

Answer 5

A ⊕ B

Question 6

How to simplify a Karnaugh map

Answer 6

• Break the expression up at the OR statements
• Plot each statement on the KMap
• Draw regions around each grouped 1. Regions should be of size of 2^n (2, 4, 8)
• If the variable remains the same, keep it

Question 7

What are the general AND rules?

Answer 7

• X AND 0 = 0
• X AND 1 = X
• X AND X = X
• NOT X AND X = 0

Question 8

What are the general OR rules?

Answer 8

• X OR 0 = X
• X OR 1 = 1
• X OR X = X
• NOT X OR X = 1

Question 9

How do you apply De Morgan’s rule?

Answer 9

• Initial statement: ¬(A ∧ B)
• Change the AND to an OR (or vice versa): ¬(A V B)
• Negate both statements in the bracket: ¬(¬A V ¬B)
• Negate the whole statement: ¬¬(¬A V ¬B)
• Double negations: (¬A V ¬B)
• Get rid of brackets: ¬A V ¬B

Question 10

How do you apply the distribution law?

Answer 10

• Initial statement: A V (B ∧ C)
• Factorise the statement: (A V B) ∧ (A V C)

Question 11

How do you apply the association law?

Answer 11

• We can remove brackets and regroup variables ONLY if the signs are the same (all OR or all AND)
• Initial statement: (A V B) V C
• Regroup variables: A V B V C

Question 12

How do you apply the commutative law?

Answer 12

• The order of the variables does not change the outcome
• A V B is the same as B V A

Question 13

How do you apply the double negation law?

Answer 13

• Two NOTs cancel eachother out
• ¬¬A is the same as A

Question 14

How does a D-type flip flop circuit work?

Answer 14

• There are 2 inputs: D and clock
• There are 2 outputs: Q and NOT Q
• On the rising edge of the clock, if D is high, Q goes high
• If D is low, Q goes low
• Values only change on the rising edge

Question 15

What is a D-type flip flop circuit?

Answer 15

• Contains 2 stable states and is used to store the state of 1 bit of data. It changes state on the edge of a clock pulse

Question 16

Explain where you would use a D-type flip flop circuit

Answer 16

• Shift registers
• Counters
• Memory units

Question 17

What is a half adder circuit?

Answer 17

• A digital circuit used to perform the addition of two single bit numbers
• Has two inputs (A and B)
• Has two outputs: Carry out (Cout) and Sum (S)

Question 18

How do you simplify the outputs of a half adder circuit?

Answer 18

• Carry out (Cout) is the same as A AND B
• Sum (S) is the same as A XOR B

Question 19

How do you draw a half adder circuit?

Answer 19

• AND gate with A and B as the input, output is Cout
• XOR gate with A and B as the input, output is S

Question 20

What is a full adder circuit?

Answer 20

• A digital circuit that allows the addition of 3 bits
• It has 3 inputs: A, B and Cin
• It has 2 outputs: Cout and Sum (S)

Question 21

How do you use a full adder circuit?

Answer 21

• Add together all the bits in the inputs. E.G: A=1, B=1, C=0. Add together 1+1=2
• Write down the answer in binary: 10
• Cout is 1 and sum is 0

Question 22

How do you draw a full adder circuit?

Answer 22

• Draw a half adder with A and B as the inputs
• Draw another half adder with the output of the first XOR gate and C as the inputs
• The output from the second XOR gate is the sum (S)
• Draw an OR gate with the outputs of both AND gates as the input. The output of this is Cout