Third Chapter Lesson-1: Concept of Number System.

At the end of this lesson-

  • 1. You will be able to describe the history of creating number.
  • 2. You will be able to distinguish number and digit. 
  • 3. You will be able to describe the types of number system.   
  • 4. You will be able to differentiate different types of number systems. 

 

A digit is a single numerical symbol, from 0 to 9. A number is a string of one or more digits.

For example, 7 is both a digit and a number. In fact, it’s a one-digit number. However, 15 is a string of two digits, so it’s a number — a two-digit number. And 426 is a three-digit number.

The value of each digit in a number can be determined using −

  • The digit
  • The position of the digit in the number
  • The base of the number system

Number system: The technique to represent and work with numbers is called number system. Decimal number system is the most common number system.

Number system is classified in two ways based on the position of the digits in a number. They are-

  • Non-Positional number system
  • Positional number system

Non-Positional number system: In Non-Positional number system, each symbol represents the same value regardless of its position.
In Non-Positional number system, each symbol represents a number with its own place value.

Example of Non-Positional number system:
Roman number system, where I for 1, III for 3 etc.

Positional number system: In Positional number system, each symbol represents different value depending on the position they occupy in a number.
In Positional number system, each system has a value that relates to the number directly next to it. The total value of a positional number is the total of the resultant value of all positions.

Different parts of a number in positional number system-

Positional number system is four types. They are-

  • Binary Number System
  • Octal Number System
  • Decimal Number System
  • Hexa Decimal Number System

Binary Number System:

A Binary number system has only two digits that are 0 and 1. Every number (value) represents with 0 and 1 in this number system. The base of binary number system is 2, because it has only two digits.

It is also called as base 2 number system. The easiest way to vary instructions through electric signals is two-state system – on and off. On is represented as 1 and off as 0, though 0 is not actually no signal but signal at a lower voltage.

Each binary digit is also called a bit. Binary number system is also positional value system, where each digit has a value expressed in powers of 2.

In any binary number, the rightmost digit is called least significant bit (LSB) and leftmost digit is called most significant bit (MSB).

Computer memory is measured in terms of how many bits it can store. Here is a chart for memory capacity conversion.

  • 1 byte (B) = 8 bits
  • 1 Kilobytes (KB) = 1024 bytes
  • 1 Megabyte (MB) = 1024 KB
  • 1 Gigabyte (GB) = 1024 MB
  • 1 Terabyte (TB) = 1024 GB
  • 1 Exabyte (EB) = 1024 PB
  • 1 Zettabyte = 1024 EB
  • 1 Yottabyte (YB) = 1024 ZB

Octal Number System:

Octal number system has only eight (8) digits from 0 to 7. Every number (value) represents with 0,1,2,3,4,5,6 and 7 in this number system. The base of octal number system is 8, because it has only 8 digits.

Octal number system is also a positional value system with where each digit has its value expressed in powers of 8.It is also called as base 8 number system.

Decimal Number System:

Decimal number system has only ten (10) digits from 0 to 9. Every number (value) represents with 0,1,2,3,4,5,6, 7,8 and 9 in this number system. The base of decimal number system is 10, because it has only 10 digits.

Decimal number system is also a positional value system. This means that the value of digits will depend on its position.

Hexa Decimal Number System:

A Hexadecimal number system has sixteen (16) alphanumeric values from 0 to 9 and A to F. Every number (value) represents with 0,1,2,3,4,5,6, 7,8,9,A,B,C,D,E and F in this number system. The base of hexadecimal number system is 16, because it has 16 alphanumeric values.

Here A is equal to 10, B is equal to 11, C is equal to 12, D is equal to 13, E is equal to 14 and F is equal to 15.

Hexadecimal number system is also a positional value system with where each digit has its value expressed in powers of 16.

Table of the Numbers Systems with Base, Used Digits, Representation:

Number systemBaseUsed digitsExample
Binary20,1(11110000)2
Octal80,1,2,3,4,5,6,7(360)8
Decimal100,1,2,3,4,5,6,7,8,9(240)10
Hexadecimal160,1,2,3,4,5,6,7,8,9,
A,B,C,D,E,F
(F0)16

Base of the number system:

  • Base of a number system is the total number of digits used in that number system.
  • Base is used as subscript of a number.
  • Number system with base ‘b’ has its digits in the range [0 , b-1].
  • It is also called as radix of a number system.

Lesson Evaluation-

Knowledge Based Questions:

  • ক। নম্বর (সংখ্যা) কি?
  • ক। ডিজিট (অংক) কি?
  • ক। সংখ্যা পদ্ধতি কী?
  • ক। পজিশনাল সংখ্যা পদ্ধতি কী?
  • ক। নন-পজিশনাল সংখ্যা পদ্ধতি কী?
  • ক। স্থানীয় মান কী?
  • ক। রেডিক্স পয়েন্ট কী?
  • ক। বাইনারি সংখ্যা পদ্ধতি কী?
  • ক। বিট/বাইট কী?
  • ক। অক্টাল সংখ্যা পদ্ধতি কী?
  • ক। ডেসিমেল সংখ্যা পদ্ধতি কী?
  • ক। হেক্সাডেসিমেল সংখ্যা পদ্ধতি কী?
  • ক। সংখ্যা পদ্ধতির বেজ বা ভিত্তি কী?

Comprehension Based Questions:

  • খ। “সকল অংকই সংখ্যা কিন্তু সকল সংখ্যা অংক নয়”- ব্যাখ্যা কর।
  • খ। “ট্যালি একটি ননপজিশনাল সংখ্যা পদ্ধতি”- ব্যাখ্যা কর।
  • খ। সংখ্যা পদ্ধতির বেজ ব্যাখ্যা কর।
  • খ। (১১)১০  সংখ্যাটিকে পজিশনাল সংখ্যা বলা হয় কেন?
  • খ। সংখ্যা পদ্ধতিতে ১০১০১ কী ধরনের সংখ্যা বর্ণনা কর।
  • খ। ৯৮৮ সংখ্যাটি কোন ধরনের সংখ্যা পদ্ধতির- ব্যাখ্যা কর।
  • খ। 3D কোন ধরনের সংখ্যা? ব্যাখ্যা কর।
  • খ। ৩ ভিত্তিক সংখ্যা পদ্ধতি- ব্যাখ্যা কর।
  • খ। (২৯৮) সঠিক কিনা- ব্যাখ্যা কর।
  • খ। “কম্পিউটারের অভ্যন্তরীণ যন্ত্রাংশের কার্যপদ্ধতির সাথে বাইনারি সংখ্যা পদ্ধতি সামঞ্জস্যপূর্ণ”- ব্যাখ্যা কর।
  • খ। কম্পিউটারের ক্ষেত্রে ডিজিটাল সিগনাল উপযোগী কেন? ব্যাখ্যা কর।
  • খ। কম্পিউটার ডিজাইনে বাইনারি সংখ্যা পদ্ধতির ব্যবহারের কারণ লেখ।
  • খ। হেক্সাডেসিমেল ও দশমিক সংখ্যা পদ্ধতির মধ্যে তুমি কিভাবে পার্থক্য করবে?
  • খ। “অক্টাল তিন বিটের কোড”- বুঝিয়ে লেখ।
  • খ। “হেক্সাডেসিমেল চার বিটের কোড” – বুঝিয়ে লেখ।

Creative Questions:

Multiple Choice Questions:

 


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