# Boolean Algebra Flashcards

1
Q

¬(¬A) =

A

A

2
Q

A∧ ¬A =

A

0

3
Q

A∨ ¬A =

A

1

4
Q

conjunction

A

AND

5
Q

disjunction

A

OR

6
Q

Exclusive disjunction

A

XOR

7
Q

Negation

A

NOT

8
Q

A

AND (*)

9
Q

A

OR (+)

10
Q

De Morgan’s Law (first)

A

¬ (A∨B) = (¬ A) ∧(¬ B)

NOT (A OR B) is the same as (NOT A) AND (NOT B)

11
Q

Distribution LAW (OR)

A
```A∧(B∨C)=(A∧B)∨(A∧C)
A AND (B OR C) is the same as (A AND B) OR (A AND C)```
12
Q

Distribution LAW (AND)

A
```A∨(B∧C)= (A∨B)∧(A∨C)
A OR (B AND C) is the same as (A OR B) AND (A OR C)```
13
Q

Association LAW (OR)

A
```A∨(B∨C)=(A∨B)∨C= A∨B∨C
A OR (B OR C) is the same as (A OR B) OR C is the same as A OR B OR C```
14
Q

Association LAW (AND

A
```A∧(B∧C)=(A∧B)∧C= A∧B∧C
A AND (B AND C) is the same as (A AND B) AND C is the same as A AND B AND C```
15
Q

commutation LAW AND

A

A∧B = B∧A

The order in which two variables are AND’ed makes no difference

16
Q

commutation LAW OR

A

A∨B = B∨A

The order in which two variables are OR’ed makes no difference

17
Q

Absorption Law AND

A
```A∨(A∧B) = A
X OR (X AND Y) is the same as X```
18
Q

Absorption Law OR

A
```A∧(A∨B)=A
X AND (X OR Y) is the same as X```
19
Q

X∧0=

A

0

20
Q

X∧1=

A

X

21
Q

X∧X=

A

X

22
Q

X∧¬X=

A

0

23
Q

X∨0 =

A

X

24
Q

X∨1 =

A

1

25
Q

X∨X=

A

X

26
Q

X∨¬X=

A

1

27
Q

AND

A

The output it true if both inputs are true, else its false

28
Q

OR

A

The output is true if 1 or both inputs are true, else the output is false

29
Q

NOT

A

reverses the input

30
Q

XOR

A

The output is true if one input is true, else the output is false

31
Q

What does binary represent?

A

the presence or absence of current

32
Q

logic gate

A

a series of electrical switches that take one or more inputs and produce a single output

33
Q

¬

A

NOT

34
Q

⊕ ⊻

A

XOR

35
Q

De Morgan’s Law (second)

A

¬ (A∧B) = (¬ A)∨(¬ B)

NOT (A AND B) is the same as (NOT A) OR (NOT B)

36
Q

Karnaugh map rules

A
• no zeros in the blocks
• no diagonal blocks
• groups as large as possible
• groups contain 2^n blocks
• overlapping blocks are allowed
• wrap around blocks are allowed
• aim for the smallest number of groups
37
Q

A

38
Q

A

inputs: the two bits to be added
outputs: the result and the carry

39
Q

logic gates in a half adder

A

XOR (to the sum)

AND (to the carry)

40
Q

A
• can only add one bit numbers

- only two inputs, the carry from a previous addition can’t be incorperated

41
Q

A

42
Q

A

inputs: the two bits to add, the previous carry bit
outputs: the result, the carry

43
Q

Flip flop

A

elemental sequential logic circuit that can store one bit and flip between two states

44
Q

Flip Flop use

A

used as a memory cell to store the state of a bit

45
Q

clock

A

sequential circuit that changes state at regular time intervals

46
Q

clock use

A

synchronise the change of state of flip flop circuits

47
Q

flip flop clock diagrams

A

on each rising edge of the clock change the result to whatever the input is (it may not need changing)

48
Q

example uses of flip flops

A
• in registers

- static RAM

49
Q

flip flop logic gates

A

Two NAND gates with two inputs. The result of of each is the second input for the other.

50
Q

D-type flip flop

A

two flip flops combined

51
Q