Boolean Algebra

Question 1

¬(¬A) =

Answer 1

A

Question 2

A∧ ¬A =

Answer 2

0

Question 3

A∨ ¬A =

Answer 3

1

Question 4

De Morgan’s Law (first)

Answer 4

¬ (A∨B) = (¬ A) ∧(¬ B)

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

Question 5

Distribution LAW (OR)

Answer 5

A∧(B∨C)=(A∧B)∨(A∧C)

A AND (B OR C) is the same as (A AND B) OR (A AND C)

Question 6

Distribution LAW (AND)

Answer 6

A∨(B∧C)= (A∨B)∧(A∨C)

A OR (B AND C) is the same as (A OR B) AND (A OR C)

Question 7

Association LAW (OR)

Answer 7

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 8

Association LAW (AND)

Answer 8

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 9

Commutation LAW AND

Answer 9

A∧B = B∧A

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

Question 10

Commutation LAW OR

Answer 10

A∨B = B∨A

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

Question 11

Absorption Law AND

Answer 11

A∨(A∧B) = A

A OR (A AND B) is the same as A

Question 12

Absorption Law OR

Answer 12

A∧(A∨B)=A

A AND (A OR B) is the same as A

Question 13

X∧0=

Answer 13

0

Question 14

X∧1=

Answer 14

X

Question 15

X∧X=

Answer 15

X

Question 16

X∧¬X=

Answer 16

0

Question 17

X∨0 =

Answer 17

X

Question 18

X∨1 =

Answer 18

1

Question 19

X∨X=

Answer 19

X

Question 20

X∨¬X=

Answer 20

1

Question 21

What does “AND” do?

Answer 21

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

used for multiplication

Question 22

What does OR do?

Answer 22

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

used for addition

Question 23

What does NOT do?

Answer 23

reverses the input

Question 24

What does XOR do?

Answer 24

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

Question 25

What is De Morgan’s Law (second)?

Answer 25

¬(A∧B) = (¬ A)∨(¬ B)

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

Question 26

What are the Karnaugh map rules?

Answer 26

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 27

what is the use of a Half adder?

Answer 27

adds two bits

Question 28

what are the Half adder outputs/inputs?

Answer 28

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

Question 29

what are the two logic gates in a half adder?

Answer 29

XOR (to the sum)

AND (to the carry)

Question 30

what are the limitations of a half-adder?

Answer 30

can only add one bit numbers

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

Question 31

what does a Full adder do?

Answer 31

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

Question 32

what are the Full adder inputs/outputs

Answer 32

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

Question 33

what is meant by Flip flop?

Answer 33

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

Question 34

what are the uses of Flip Flop?

Answer 34

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

Question 35

what is meant by a clock?

Answer 35

sequential circuit that changes state at regular time intervals

Question 36

what are the uses of a clock?

Answer 36

synchronise the change of state of flip flop circuits

Question 37

flip flop clock diagrams

Answer 37

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

Question 38

example uses of flip flops

Answer 38

in registers
- static RAM

Question 39

flip flop logic gates

Answer 39

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

Question 40

What is meant by a D-type flip flop

Answer 40

two flip flops combined

Question 41

how is a full adder different to a half adder?

Answer 41

a full adder is two half adders which is able to add 4-bit binary numbers.

Question 42

how can yuou make a full adder?

Answer 42

2 half adders can be joined together with an “OR” gate to form a full adder