Unit 8 - Boolean Algebra Flashcards

1
Q

shape of AND gate and AND symbol

A

shape = D
symbol = ^

2
Q

shape of NOT gate and NOT symbol

A

shape = triangle
symbol = ¬

3
Q

shape of OR gate and OR symbol

A

shape = curved triangle thing
symbol = v

4
Q

shape of XOR gate and XOR symbol

A

shape = OR gate with extra line
symbol = v̲

5
Q

what is de Morgan’s first law

A

¬(A v B) = ¬A ^ ¬ B

6
Q

what is de Morgan’s second law

A

¬(A ^ B) = ¬A v ¬B

7
Q

what are the 8 general rules of boolean algebra

A
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
8
Q

X ^ 0 = ?

A

0

9
Q

X ^ 1 = ?

A

X

10
Q

X ^ X = ?

A

X

11
Q

X ^ ¬X = ?

A

0

12
Q

X v 0 = ?

A

X

13
Q

X v 1 = ?

A

1

14
Q

X v X = ?

A

X

15
Q

X v ¬X = ?

A

1

16
Q

what are the commutative rules

A
1. X ^ Y = Y ^ X
2. X v Y = Y v X
17
Q

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

A

Y ^ X
commutative

18
Q

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

A

Y v X
commutative

19
Q

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

A

¬A ^ ¬ B
de Morgan’s first law

20
Q

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

A

¬A v ¬ B
de Morgan’s second law

21
Q

what are the associative rules

A
1. X ^ ( Y ^ Z) = (X ^ Y) ^ Z
2. X v (Y v Z) = (X v Y) v Z
22
Q

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

A

(X ^ Y) ^ Z
associative

23
Q

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

A

(X v Y) v Z
associative

24
Q

what are the distributive rules

A
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)
25
Q

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

A

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

26
Q

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

A

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

27
Q

what are the absorption rules

A
1. X v (X ^ Y) = X
2. X ^ (X v Y) = X
28
Q

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

A

X
absorption

29
Q

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

A

X
absorption

30
Q

what is the double negation rule

A
1. X = ¬¬X
31
Q

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

A

X
double negation

32
Q

what is a karnaugh map

A

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

33
Q

K-MAPS: sizes of groupings that are allowed

A

1, 2, 4 or 8 and can be overlapping

34
Q

K - MAPS: determining groupings

A

each grouping should be as large as possible

35
Q

A

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

36
Q

A

sum

37
Q

A

carry bit

38
Q

A

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

39
Q

logic gate circuit for half adder

A
40
Q

A
41
Q

what is a D-type flip-flop

A

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).

42
Q

what does an edge-triggered flip-flop mean

A

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

43
Q

uses of D-type flip-flops

A
• 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
44
Q

what does a D-type flip-flop look like

A