Boolean Algebra Laws

Question 1

Boolean Logic

Answer 1

Named after the nineteenth-century mathematician George Boole, it is a form of algebra in which all values are reduced to either TRUE or FALSE.

Question 2

Karnaugh Maps

Answer 2

Method to simplify Boolean algebra expressions, leveraging pattern recognition to minimize calculations. Reduces real-world logic requirements for efficient implementation with minimal logic gates.

Question 3

Boolean Algebra

Answer 3

A set of rules for manipulating truth values according to truth tables. Very important in computing as truth values in Boolean algebra are True and false, and can thus easily be represented as the binary digits 1 and 0.

Question 3

De Morgan’s Law

Answer 3

Two laws stating the duality of AND and OR operations. In English: 1) ‘Not (A and B)’ equals ‘(Not A) or (Not B)’ and 2) ‘Not (A or B)’ equals ‘(Not A) and (Not B)’. Designed to simplify electronic circuit design.”

Question 4

Distribution

Answer 4

A rule or law in Boolean algebra which permits the multiplying or factoring out of an expression.

Question 5

Association

Answer 5

A rule or law in Boolean algebra which permits the removal of brackets from an expression and regrouping of the variables.

Question 6

Commutation

Answer 6

A rule or law in Boolean algebra which stats that the order of application of two separate terms is not important: A AND B = B AND A

Question 7

Double Negation

Answer 7

A rule or law in Boolean algebra where if you invert a term twice it is equal to its original term: (NOT NOT A) = A

Question 8

Logic Gate Diagram

Answer 8

A method of expression Boolean Logic in a diagrammatic form using a set of standard symbols representing the various Logic Gates such as AND NOT OR NAND etc.

Question 9

Truth Table

Answer 9

A notation used in Boolean algebra for defining the output of a logic gate or logic circuit for all possible combinations of inputs.

Question 10

D Type Flip Flops

Answer 10

Also known as a data or delay flip flop. This is a circuit or logic design which can be viewed as a memory cell. It has two stable states. Using appropriate input signals, you can trigger the flip-flop from one state to the other.

Question 10

Half Adders

Answer 10

A unit which adds together two input variables. A half adder can only add the inputs together.

Question 11

Full Adders

Answer 11

A unit which adds together two input variables. A full adder can a bit carried from another addition as well as the two inputs.

Question 11

Simplify the Equation:

(A.B)+A

Answer 11

. Take out the common factor A
A(B+1)
Use identity 1+A = 1
A(1) or A.1
2. Use identity A.1=A
3. Answer = A

Question 12

Simplify the Equation:
(A+B).(A+A)

Answer 12

1. Use Identity Law A+A = A (A+B).A
2. Multiply out A.A+A.B
3. Use Identity Law A.A = A A+(B.A)
4. Use redundancy law A+(A.B) = A A

Question 12

Simplify the Equation:
B.(A+A.B)

Answer 12

1. Multiply out (B.A)+(B.A.B)
2. Simplify right-hand side
   (B.A.B) = A.B (B.A)+(A.B)
3. Commutative Law A.B