Unit 8 - Boolean Algebra

Question 1

shape of AND gate and AND symbol

Answer 1

shape = D
symbol = ^

Question 2

shape of NOT gate and NOT symbol

Answer 2

shape = triangle
symbol = ¬

Question 3

shape of OR gate and OR symbol

Answer 3

shape = curved triangle thing
symbol = v

Question 4

shape of XOR gate and XOR symbol

Answer 4

shape = OR gate with extra line
symbol = v̲

Question 5

what is de Morgan’s first law

Answer 5

¬(A v B) = ¬A ^ ¬ B

Question 6

what is de Morgan’s second law

Answer 6

¬(A ^ B) = ¬A v ¬B

Question 7

what are the 8 general rules of boolean algebra

Answer 7

1. X ^ 0 = 0
2. X ^ 1 = X
3. X ^ X = X
4. X ^ ¬X = 0
5. X v 0 = X
6. X v 1 = 1
7. X v X = X
8. X v ¬X = 1

Question 8

X ^ 0 = ?

Answer 8

0

Question 9

X ^ 1 = ?

Answer 9

X

Question 10

X ^ X = ?

Answer 10

X

Question 11

X ^ ¬X = ?

Answer 11

0

Question 12

X v 0 = ?

Answer 12

X

Question 13

X v 1 = ?

Answer 13

1

Question 14

X v X = ?

Answer 14

X

Question 15

X v ¬X = ?

Answer 15

1

Question 16

what are the commutative rules

Answer 16

1. X ^ Y = Y ^ X
2. X v Y = Y v X

Question 17

simplify, reorganise or expand X ^ Y = ? and name the rule used

Answer 17

Y ^ X
commutative

Question 18

simplify, reorganise or expand X v Y = ? and name the rule used

Answer 18

Y v X
commutative

Question 19

simplify, reorganise or expand ¬(A v B) = ? and name the rule used

Answer 19

¬A ^ ¬ B
de Morgan’s first law

Question 20

simplify, reorganise or expand ¬(A ^ B) = ?and name the rule used

Answer 20

¬A v ¬ B
de Morgan’s second law

Question 21

what are the associative rules

Answer 21

1. X ^ ( Y ^ Z) = (X ^ Y) ^ Z
2. X v (Y v Z) = (X v Y) v Z

Question 22

simplify, reorganise or expand X ^ ( Y ^ Z) = ? and name the rule used

Answer 22

(X ^ Y) ^ Z
associative

Question 23

simplify, reorganise or expand X v ( Y v Z) = ? and name the rule used

Answer 23

(X v Y) v Z
associative

Question 24

what are the distributive rules

Answer 24

1. X ^ (Y v Z) = (X ^ Y) v (X ^Z)
2. (X v Y) ^ (W v Z) = (X ^ W) v ( X ^ Z) v (Y ^ W) v (Y ^ Z)

Question 25

simplify, reorganise or expand X ^ (Y v Z) = ? and name the rule used

Answer 25

(X ^ Y) v (X ^Z) distributive

Question 26

simplify, reorganise or expand (X v Y) ^ (W v Z) = ? and name the rule used

Answer 26

(X ^ W) v ( X ^ Z) v (Y ^ W) v (Y ^ Z) distributive

Question 27

what are the absorption rules

Answer 27

1. X v (X ^ Y) = X 2. X ^ (X v Y) = X

Question 28

simplify, reorganise or expand X v (X ^ Y) = ? and name the rule used

Answer 28

X absorption

Question 29

simplify, reorganise or expand X ^ (X v Y) = ? and name the rule used

Answer 29

X absorption

Question 30

what is the double negation rule

Answer 30

1. X = ¬¬X

Question 31

simplify, reorganise or expand ¬¬X = ? and name the rule used

Answer 31

X double negation

Question 32

what is a karnaugh map

Answer 32

an alternative way of simplifying boolean expressions which is often easier than using boolean algerbra for those using up to three of four variables. it is similar to a truth table and allows us to easily detect grouping with common factors

Question 33

K-MAPS: sizes of groupings that are allowed

Answer 33

1, 2, 4 or 8 and can be overlapping

Question 34

K - MAPS: determining groupings

Answer 34

each grouping should be as large as possible

Question 35

what is a half-adder

Answer 35

a half adder can take an input of two-bits and give a two-bit output as a correct result of an addition of the two bits

Question 36

adders: what does S represent

Answer 36

sum

Question 37

adders: what does C represent

Answer 37

carry bit

Question 38

what is a full adder

Answer 38

a full adder combines two half adders to add three bits together including the two inputs A and B, and the carry bit

Question 39

logic gate circuit for half adder

Answer 39

Question 40

logic gate of full adder

Answer 40

Question 41

what is a D-type flip-flop

Answer 41

a flip flop is an element sequential logic circuit that can store one bit and flip between two states, 0 and 1. a D-type flip flop has one input called D, and two output Q and NOT Q (a clock signal).

Question 42

what does an edge-triggered flip-flop mean

Answer 42

it stores the value of one bit when a signal is given - takes in three inputs the clock, D and Q and then on the rising edge of the clock Q will change to D

Question 43

uses of D-type flip-flops

Answer 43

- D-type flip-flops are used for creating registers and counters - they are used for intermediate storage needed during arithmetic operations - static RAM is also created using D-type flip-flops

Question 44

what does a D-type flip-flop look like

Answer 44