Computer Basics -5 || Understanding of Number System.

All the processes in the digital world are the game of numbers. To manage all this process and providing the information is called the Number System.

Most commonly used number system is the Decimal Number System (base 10). Which we have used in general life also. Other major number systems are the Binary Number System(base 2), Octal Number System(base 8), Hexadecimal Number System(base 16).

Remember, we have learned the first thing in our school was A to Z, अ, आ, इ, ई. Then we moved to words, sentences, paragraphs and so on.

It means to write any language we need a few standard basic symbols. These symbols or characters are collectively known as Script or लिपि. Like for the Hindi language was written in देवनागरी script. The same way for any number system there is a predefined script present which is known as the base of the number system.

Decimal Number System

Decimal Number system has a base 10 number system. This includes 0 to 9 digits. It means all the values written in the Decimal Number System would contain 0 to 9 digits only.

The value of these digits (0 to 9) will depend on the position of the digit. That’s why it is also known as a positional value system.

For example, consider three numbers 123, 213, 231. Here we can see there are three numbers having the same digits but the value of these numbers are different.

  • 123: the value of 1 is 100 (One hundred twenty-three)
  • 213: the value of 1 is 10 (Two hundred thirteen)
  • 231: the value of 1 is 1 (Two hundred thirty-one)

The value or weightage of each position can be understandable by the below image.

Decimal Number System

As we all know that in any computer system instructions have been passed through the electric signals. So while using Decimal Number System we have to 10 signals for single instructions, that is too complex. So, other number systems have been developed to make it easier to implement by reducing the base.

Binary Number System

The easiest way to resolve the above problem is by using the Binary Number System. Most of the technologies use this system. This number system works on base 2. Means only two numbers 0 and 1 used in this number system. That’s why it is called a Binary Number System.

  • 0 = OFF
  • 1 = ON

All the values would be defined using these two digits (0 and 1) in the Binary number system. Like the Decimal Number System, these are also using Positional Value System.

Binary to Decimal

Suppose that any digital system received two signals like 101 and 010. So we could get the actual value by using below method:

Binary Number System

Each digit is called a unit of memory bit in Binary Number System. Computer memory is measured in terms of how many bits it can store.

Memory Chart
Memory Chart

Decimal to Binary

Decimal  to Binary Conversion
Decimal to Binary Conversion

Octal Number System

Octal Number System has base 8. It contains digits from 0 to 7. Likewise Decimal and Binary Number systems we can get decimal value from an Octal Value.

Octal to Decimal

Octal Value: 6728

6728 = (82 x 6) + (81 x 7) + (80 x 2)
         = 384 + 56 + 2
         = 44210

Decimal to Octal

Decimal to Octal Conversion
Decimal to Octal Conversion

Hexadecimal Number System

Hexadecimal Number System has base 16. It contains digits from 0 to 9 and A to F. Remember A=10, B=11, C=12 and so on.

Hexadecimal to Decimal

Hexadecimal Value: 6F216

6F216 = (162 x 6) + (161 x 15) + (160 x 2)
         = 1536 + 240 + 2
         = 177810

Decimal to Hexadecimal

Hexadecimal to Decimal Conversion

ASCII

Below are the complete set of letters and symbols used in any standard computer system.

  • Lower Case Alphabets (a to z) : 26
  • Upper Case Alphabets (A to Z) : 26
  • Numeric Values (0 to 9) : 10
  • Punctuation Marks(. , ; : – ” !) : 7
  • Special Characters (like $ @ & etc) : approx 40

These computer systems are now used Globally all over the world. So, it is necessary that there should be a unique value assigned to each of the above letter or symbols.

As we know that all the data/information, instructions is stored on a computer in binary form. So, assigning a standard Binary Code to each of them has been done under the ASCII code. It stands for American Standard Code for Information Interchange.

LetterASCII CodeBinaryLetterASCII CodeBinary
a971100001A651000001
b981100010B661000010
c991100011C671000011
d1001100100D681000100
e1011100101E691000101
f1021100110F701000110
g1031100111G711000111
h1041101000H721001000
i1051101001I731001001
j1061101010J741001010
k1071101011K751001011
l1081101100L761001100
m1091101101M771001101
n1101101110N781001110
o1111101111O791001111
p1121110000P801010000
q1131110001Q811010001
r1141110010R821010010
s1151110011S831010011
t1161110100T841010100
u1171110101U851010101
v1181110110V861010110
w1191110111W871010111
x1201111000X881011000
y1211111001Y891011001
z1221111010Z901011010

ISCII

The same way ISCII (Indian Standard Code for Information Interchange) has been developed to support Devanagari, Tamil, Bangla, Gujarati, etc.

Microprocessor

Microprocessor is like a brain of Computer. It controls entire system on a single chip. The design and functioning on the microprocessors are different depending upon the machine type.

While selecting any computer system, be careful about below characteristics of Microprocessors:

  • Clock Speed
  • Word Size
  • Instruction Set

Clock Speed

Clock Speed defines the speed of the microprocessor at which it executes the instructions. Speed of any microprocessor depends on how many electric signals can be transferred per second. That’s why Clock Speed is measured in MHz(Mega Hertz) or GHz(Giga Hertz).

  • 1 MHz = 1 Million cycle per second
  • 1 GHz = 1 Billion cycle per second
    • Cycle = 1 electric signal

Word Size

Word Size refers to the number of bits, that can be processed in a single instruction. The first microprocessor was a 4-bit processor. This processor has 4 input pins and 4 output pins. It means 4-bit data can be processed in a single go.

Nowadays, 32-bit and 64-bit microprocessor available in the market.

Instruction Set

Instructions are the commands to perform an action/operation on the given set of Data.

There are few pre-defined instructions are present in the Microprocessor. These instructions are in Machine Language. All these instructions are known as Instruction Set. Few of them are mentioned below:

  • Data Transfer: share data, transform into information, etc.
  • Arithmetic Operations: Basic Calculations
  • Logical Operations: Decision making
  • Control Flow: Handling Memory, Processes, etc.
  • Input/Output and Machine Control

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