COMPUTER ORGANIZATION AND

ASSEMBLY LANGUAGE

LECTURE BASED ON BOOLEAN EXPRESSIONS FOR

COMBINATIONAL LOGICSEPTEMBER 20, 2013

IMPORTANT NOTE

Please fastened your seat belt as we have to reach our destination in one hour. Be as quick as you can, if we don’t reach our destination I have to throw you out of the aircraft and you will not be provided with the life saving jackets.

The aircraft is a five star aircraft not like a local plane so you have all the facilities and you can’t complain about the services.

BOOLEAN ALGEBRA

Because you all are competent and hardworking students I am positive that you all know the significance of Boolean Algebra specifically in the Computer Organization and Assembly Language context.

Prove me right by letting me know what is your understanding regarding the Boolean Algebra and tell me its significance in terms of Design Complexity.

BOOLEAN EXPRESSIONS OF COMBINATIONAL LOGIC

What is the role of Mathematical Algebra in Computer Organization?

If it is said that Mathematical expressions are used to explain the complexity of a design by combining multiplication and addition, what would you say?

You all must say yes because it is used. If not than raise your hand and I will not mark your presence.

If you are asked to solve this expression how will you solve. Y= X. (X + 5) + 3

ANALYZE A CIRCUIT

Given below is a sample of Multi-Level Combinational Logic. You have to write the Boolean Algebra form.

EXAMPLE

Consider a comparison below, you will notice that if you don’t follow the appropriate rules your whole logic will collapse.

Try to give inputs and perform the operation you will notice that both of the logical diagrams will give you entirely different outputs.

WHY TO UNDERSTAND?

To understand Boolean Algebra logic is very vital because normally as a user we think about mathematical solution. You will notice that some expressions that work perfect in mathematics are not applicable in Boolean expressions.

Try to give inputs and solve it both in mathematical form and Boolean Algebra form.

EXAMPLE TIME

Lets do an Example now. It is indeed a more complex example as

compared to the previous one. Try to make the schematic diagram of

the expression and analyze yourself what you have done, logically.

LAWS OF BOOLEAN ALGEBRA

The manipulation of the algebraic expressions is based on the fundamental laws.

Some of these laws extended to manipulation of the Boolean Expressions.

Do you know what is a commutative law, if no raise your hands and I will send you back to govt. high school in class 8 but I can’t give you the surety they will accept you.

TO UNDERSTAND THE LOGIC OF A TRUTH TABLE

Given below is a truth table presentation. Tell me what is the logic?

FUNDAMENTAL LAWS OF BOOLEAN ALGEBRA

The three laws that are fundamental in Boolean Algebra are;

1. Associative law2. Commutative law3. Distributive law

If you have three inputs A, B and C respectively and the Output is presented by X, Can you write the expressions for the above three laws for both addition and multiplication.

RULES OF BOOLEAN ALGEBRA

There are some rules for Boolean Algebra. The rules are for NOT, AND, OR and XOR Gates.

Rule for NOT Gate? What you have to do is to have OR, AND

& XOR Gates and solve this expressions by making truth tables.

A+0= ? A+1 = ? A+ A = ? & A + A not =?

A.0= ? A.1 = ? A. A = ? & A . A not =? Use the similar logic for XOR Gate.