1.4.3 Boolean Algebra

Question 1

How can problems be defined?

Answer 1

Using boolean logic in boolean equations

Question 2

What results can come from a boolean equation?

Answer 2

True
False

Question 3

What is the name given to the conjunction operation?

Answer 3

AND

Question 4

What is the symbol given to the conjunction operation?

Answer 4

ʌ

Question 5

What is the shape given to the conjunction operation?

Answer 5

D

Question 6

What is the name given to the disjunction operation?

Answer 6

OR

Question 7

What is the symbol given to the disjunction operation?

Answer 7

V

Question 8

What is the name given to the negation operation?

Answer 8

NOT

Question 9

What is the symbol given to the negation operation?

Answer 9

¬

Question 10

What is the shape given to the negation operation?

Answer 10

▷

Question 11

What name is given to the exclusive disjunction operation?

Answer 11

XOR

Question 12

What symbol is given to the exclusive disjunction operation?

Answer 12

V̲

Question 13

What is a truth table?

Answer 13

A table showing every possible combination of inputs to a logic gate and corresponding output

Question 14

How are boolean equations made?

Answer 14

By combining boolean operators

Question 15

What is a Karnaugh map?

Answer 15

A method of simpiflying boolean expressions

Question 16

Describe how boolean expressions can be simplified using Karnaugh map.

Answer 16

Write truth table as a Karnaugh map
Highlight groups of 1s in map
Remove variables which change within rectangles
Keep variables which do not change

Question 17

How can expressions be simplified using De Morgan’s Law?

Answer 17

¬(A ʌ B) = ¬A v ¬B
¬(A v B) = ¬A ʌ ¬B

Question 18

How can expressions be simplified using Distribution Law?

Answer 18

A ʌ (B v C) = (A ʌ B) v (A ʌ C)
A v (B ʌ C) = (A v B) ʌ (A v C)
A ʌ (B ʌ C) = (A ʌ B) ʌ (A ʌ C)
A ʌ (B v C) = (A v B) v (A v C)

Question 19

How can expressions be simplified using Association Law?

Answer 19

(A ʌ B) ʌ C = A ʌ (B ʌ C) = A ʌ B ʌ C
(A v B) v C = A v (B v C) = A v B v C

Question 20

How can expressions be simplified using Commutation Law?

Answer 20

A v B = B v A
A ʌ B = B ʌ A

Question 21

How can expressions be simplified using Double Negation Law?

Answer 21

¬¬A = A

Question 22

What is the purpose of a D-type flip flop?

Answer 22

To store the value of a single bit

Question 23

When is the stored value in a D-type flip flop updated?

Answer 23

On the rising edge of the clock signal

Question 24

Which logic gates are used in the logic circuit of a D-type flip flop?

Answer 24

4 NAND gates

Question 25

What two inputs are taken in the logic gate of a D-type flip flop?

Answer 25

Control signal
Clock

Question 26

What are adders?

Answer 26

Logic circuits which add together the number of inputs which are True

Question 27

What two inputs are taken in the logic gate of a half adder?

Answer 27

A
B

Question 28

What two outputs are produced in the logic gate of a half adder?

Answer 28

Sum
Carry

Question 29

Which logic gates are used in the logic circuit of a half adder?

Answer 29

AND
XOR

Question 30

What values are output by a half adder when both A & B are false?

Answer 30

Sum is False
Carry is False

Question 31

What values are output by a half adder when A is True and B is False?

Answer 31

Sum is True
Carry is False

Question 32

What values are output by a half adder when A is False and B is True?

Answer 32

Sum is True
Carry is False

Question 33

What values are output by a half adder when both A & B are True?

Answer 33

Sum is False
Carry is True

Question 34

What three inputs are taken in the logic gate of a full adder?

Answer 34

A
B
Carry (in)

Question 35

What two outputs are produced in the logic gate of a full adder?

Answer 35

Sum
Carry (out)

Question 36

Which logic gates are used in the logic circuit of a full adder?

Answer 36

2 XOR gates
2 AND gates
OR gate