Number System Notes

Get the notes of the Number System subject. These will be helpful in preparing for GATE exams and also your semester exams. In this article, we will take a look at number system notes. Read ahead to learn more.

Table of Contents

Number System Notes
Introduction
Number System Conversions

Two primary types of number systems exist:

Positional
Non-positional

The positional system utilises digits to represent the numbers. On the other hand, a non-positional number system utilises specific symbols to represent the numbers. For instance, octal is a positional type of number system that has the base 8.

Introduction

The binary number system that has only two independent digits is referred to as a base-2 number system. All the larger types of binary numbers get represented in terms of ‘1’ and ‘0’. Check out more on types of number systems here.

The four most generally used number systems are these:

1. Decimal

2. Binary

3. Octal

4. Hexadecimal

Number System Conversions

Check out detailed notes for each of these here:

1. Decimal to Binary Conversion – We divide the number by 2, divide the quotient by 2, repeat the process till we get 0 in the quotient. The values of the remainders in this process will be the answer that we require. Check out more on Decimal to Binary Conversion here.

2. Decimal to Hexadecimal Conversion – We divide the number by 16, divide the quotient by 16, repeat the process till we get 0 in the quotient. The values of the remainders in this process will be the answer that we require. Check out more on Decimal to Hexadecimal Conversion here.

3. Decimal to Octal Conversion – We divide the number by 8, divide the quotient by 8, repeat the process till we get 0 in the quotient. The values of the remainders in this process will be the answer that we require. Check out more on Decimal to Octal Conversion here.

4. Conversion to Base 10 – For converting to base 10, we divide it by base, get the remainder, divide the quotient by the new base, repeat this process unless the quotient is less than the base. Check out more on Conversion to Base 10 here.

5. Converting Any Base to Any Other Base – We divide the number by the base, divide the quotient by that base, repeat the process till we get 0 in the quotient. The values of the remainders in this process will be the answer that we require. Check out more on Converting Any Base to Any Other Base here.

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Number System Notes