Boolean Algebra

Question 1

¬(¬A) =

Answer 1

A

Question 2

A∧ ¬A =

Answer 2

0

Question 3

A∨ ¬A =

Answer 3

1

Question 4

conjunction

Answer 4

AND

Question 5

disjunction

Answer 5

OR

Question 6

Exclusive disjunction

Answer 6

XOR

Question 7

Negation

Answer 7

NOT

Question 8

∧

Answer 8

AND (*)

Question 9

∨

Answer 9

OR (+)

Question 10

De Morgan’s Law (first)

Answer 10

¬ (A∨B) = (¬ A) ∧(¬ B)

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

Question 11

Distribution LAW (OR)

Answer 11

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

Question 12

Distribution LAW (AND)

Answer 12

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

Question 13

Association LAW (OR)

Answer 13

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

Question 14

Association LAW (AND

Answer 14

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

Question 15

commutation LAW AND

Answer 15

A∧B = B∧A

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

Question 16

commutation LAW OR

Answer 16

A∨B = B∨A

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

Question 17

Absorption Law AND

Answer 17

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

Question 18

Absorption Law OR

Answer 18

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

Question 19

X∧0=

Answer 19

0

Question 20

X∧1=

Answer 20

X

Question 21

X∧X=

Answer 21

X

Question 22

X∧¬X=

Answer 22

0

Question 23

X∨0 =

Answer 23

X

Question 24

X∨1 =

Answer 24

1

Question 25

X∨X=

Answer 25

X

Question 26

X∨¬X=

Answer 26

1

Question 27

AND

Answer 27

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

Question 28

OR

Answer 28

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

Question 29

NOT

Answer 29

reverses the input

Question 30

XOR

Answer 30

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

Question 31

What does binary represent?

Answer 31

the presence or absence of current

Question 32

logic gate

Answer 32

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

Question 33

¬

Answer 33

NOT

Question 34

⊕ ⊻

Answer 34

XOR

Question 35

De Morgan’s Law (second)

Answer 35

¬ (A∧B) = (¬ A)∨(¬ B)

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

Question 36

Karnaugh map rules

Answer 36

• 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

Question 37

Half adder use

Answer 37

adds two bits

Question 38

Half adder outputs/inputs

Answer 38

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

Question 39

logic gates in a half adder

Answer 39

XOR (to the sum)

AND (to the carry)

Question 40

limitations of half adders

Answer 40

• can only add one bit numbers

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

Question 41

Full adder

Answer 41

combines two half adders, used to add a series of bits

Question 42

Full adder inputs/outputs

Answer 42

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

Question 43

Flip flop

Answer 43

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

Question 44

Flip Flop use

Answer 44

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

Question 45

clock

Answer 45

sequential circuit that changes state at regular time intervals

Question 46

clock use

Answer 46

synchronise the change of state of flip flop circuits

Question 47

flip flop clock diagrams

Answer 47

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

Question 48

example uses of flip flops

Answer 48

• in registers

- static RAM

Question 49

flip flop logic gates

Answer 49

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

Question 50

D-type flip flop

Answer 50

two flip flops combined

Question 51

how is a full adder different to a half adder?

Answer 51

a full adder is two half adders which is able to add three bits: the two inputs from the first half adder and the carry.