**Related Content:** CS101 - VU Lectures, Handouts, PPT Slides, Assignments, Quizzes, Papers & Books of Introduction to Computing

During that lecture we learnt about the function of the central component of a
computer, the microprocessor

And its various sub-systems

Bus interface unit

Data & instruction cache memory

Instruction decoder

ALU

Floating-point unit

Control unit

To become familiar with number system used by the microprocessors - binary numbers

To become able to perform decimal-to-binary conversions

To understand the NOT, AND, OR and XOR logic operations – the fundamental
operations that are available in all microprocessors

(BASE 2)

numbers

(BASE 10)

numbers

Decimal (base 10) number system consists of 10 symbols or digits

0 1 2 3 4

5 6 7 8 9

Binary (base 2) number system consists of just two

0 1

**Other popular number systems
Octal**

base = 8

8 symbols (0,1,2,3,4,5,6,7)

**Hexadecimal**

base = 16

16 symbols (0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F)

positional notation

in the positional notation

the positional notation

the positional notation

the positional notation

Because this system is natural for digital computers

The fundamental building block of a digital computer – the switch – possesses two
natural states, ON & OFF.

It is natural to represent those states in a number system that has only two symbols, 1
and 0, i.e. the binary number system

In some ways, the decimal number system is natural to us humans. Why?

bit

binary digit

Byte = 8 bits

Decimal Binary conversion

That finishes our first topic - introduction to binary numbers and their conversion to
and from decimal numbers

O**ur next topic is …**

Let x, y, z be Boolean variables. Boolean variables can only have binary values i.e., they
can have values which are either 0 or 1.

For example, if we represent the state of a light switch with a Boolean variable x, we will
assign a value of 0 to x when the switch is OFF, and 1 when it is ON

A few other names for the states of these Boolean variables

We define the following logic operations or functions among the Boolean variables

We’ll define these operations with the help of truth tables

what is the truth table of a logic function

A truth table defines the output of a logic function for all possible inputs

Truth Table for the** NOT Operation**

(y true whenever x is false)

Truth Table for the NOT Operation

Truth Table for the AND Operation

(z true when both x & y true)

Truth Table for the AND Operation

Truth Table for the OR Operation

(z true when x or y or both true)

Truth Table for the OR Operation

Truth Table for the XOR Operation

(z true when x or y true, but not both)

Truth Table for the XOR Operation

Those 4 were the fundamental logic operations. Here are examples of a few more complex situations

z = (x + y)´

z = y · (x + y)

z = (y · x) ⊕ w

z = (x + y)´

**Number of rows in a truth table?**

2n

n = number of input variables

About the binary number system, and how it differs from the decimal system

Positional notation for representing binary and decimal numbers

A process (or algorithm) which can be used to convert decimal numbers to binary
numbers

Basic logic operations for Boolean variables, i.e.** NOT, OR, AND, XOR, NOR, NAND, XNOR** Construction of truth tables (How many rows?)

Next lecture will be the 3rd on Web dev

The focus of the one after that, the 10th lecture, however, will be on software. During
that lecture we will try:

To understand the role of software in computing

To become able to differentiate between system and application software