1.4.3 Boolean Algebra

Question 1

1.4.3 A)
What are the four main logic gates

Answer 1

AND
OR
NOT
XOR

Question 2

1.4.3 A)
What is the symbol and operation of the AND logic gate.

Answer 2

Conjunction
symbol - ^

Question 3

1.4.3 A)
What is the symbol and operation of the OR logic gate.

Answer 3

Disjunction
symbol - V

Question 4

1.4.3 A)
What is the symbol and operation of the NOT logic gate.

Answer 4

Negation
symbol - ¬

Question 5

1.4.3 A)
What is the symbol and operation of the XOR logic gate. Gate look

Answer 5

DIsjunction
symbol - ⊻
the gate looks like a or gate with a line at the font (check notes)

Question 6

1.4.3 B)
What do truth tables show

Answer 6

all possible permuations of in input.

Question 7

1.4.3 B)
truth table for AND, where a and b are inputs and y is the output

Answer 7

A B Y
0 0 0
0 1 0
1 0 0
1 1 1

Question 8

1.4.3 B)
truth table for OR, where a and b are inputs and y is the output

Answer 8

A B Y
0 0 0
0 1 1
1 0 1
1 1 1

Question 9

1.4.3 B)
truth table for NOT, where a is the input and y is the output

Answer 9

A Y
0 1
1 0

Question 10

1.4.3 B)
truth table for XOR, where a and b are inputs and y is the output

Answer 10

A B Y
0 0 0
0 1 1
1 0 1
1 1 0

Question 11

1.4.3 B)
How do you know how many inputs are needed for a table

Answer 11

2^n where n is the number of inputs.

Question 12

1.4.3 B)
What is the need to simplify Boolean expressions

Answer 12

Logic gates represent electrical circuits, so its important to use as little as possbile.

reduce size of the circuit
reduce cost
reduce power consumption
quicker execution

Question 13

1.4.3 B)
Karnaugh maps

Answer 13

just check notes

Question 14

1.4.3 C)
What is demogans law

Answer 14

Involves breaking a negative and dchaing the operation.

¬(A∪B)= ¬A∩¬B
¬(A∩B) = ¬A∪¬B

Question 15

1.4.3 C)
What is the distribution rule

Answer 15

conjunction over disjunction

A^(BvC) = (A^B)V(A^C)

disjunction of conjunction

AV(BvC) = (AVB)^(AVC)

Question 16

1.4.3 C)
What is the association law

Answer 16

(A^B)^c = A^(B^C)
(AVB)Vc = AV(BVC)

Question 17

1.4.3 C)
commutation

Answer 17

order doesnt matter
AVB = BVA
B^A = A^B

Question 18

1.4.3 C)
double negative law

Answer 18

¬¬ A = A

Question 19

1.4.3 E)
What is a D-type flip flops

Answer 19

Logic circuit which can store the value of 1 bit.

Question 20

1.4.3 E)
How does D-type flip flops work.

inputs and outputs

Answer 20

Has 2 inputs control signal and clock input. A clock is a regular pulse generated by CPU used to coordinate components.

A clock pulse rises and falls (shown in notes).

The output can only change at a rising edge. the start of a clock tick.

Question 20

1.4.3 E)
What is an adder

Answer 20

Is a logic circuit which adds together the number of inputs.

Question 21

1.4.3 E)
Half adder

Answer 21

Two inputs and two outputs (diagram in notes + truth table)

Question 21

1.4.3 E)
Full adder

Answer 21

Three inputs and 2 outputs allows for a carry to be represented. (diagram in notes + truth table)