Number Theory for Programmers

Name: Number Theory for Programmers
Rating: 4.6 (85 reviews)

Basic Number Theory - Decimal, binary, 2's complement, Octal, Hexadecimal, IEEE 754 single and double precision.

Highest Rated

Created byShibaji Paul

Last updated 11/2019

English

What you'll learn

Understanding different number systems like Octal, Hexadecimal and Binary. How binary number system is used to represent values in memory of computer.
Understanding complement technique, signed integer represented using 2s complement in memory. Calculating range of values for signed and unsigned system.
How to perform addition and subtraction in different number system.
How the real numbers are represented using IEEE 754 single and double precision formats.
How to create a customised number system of your own.

Course content

8 sections • 30 lectures • 2h 36m total length

Introduction2:42
Introduction to the course. What is the goal, what you will learn.

Understanding Octal Number. Octal to Decimal Conversion.7:55
Learn how numbers are represented using Octal System also understand how we can convert an Octal number to equivalent Decimal Number.
Quiz 4
Let's now learn how to convert a Decimal integer into equivalent Octal.5:44
Learn how we can convert a Decimal integer number to equivalent Octal number. Also you will see that the idea of converting Decimal to any other number system is actually a generic idea.
Quiz 5
Convert Octal number with fractional part (That is with Radix point) to decimal.5:13
Let's now understand how we can convert an Octal number with a radix point to equivalent decimal.
Quiz 6
How to convert real decimal number with decimal point to equivalent Octal.4:15
Let us now learn how we can convert a real decimal number with a decimal point to equivalent Octal.
Quiz 7
Procedure for adding Octal numbers.2:48
Learn how to add 2 octal numbers. You will find that the procedure is just same as we follow while adding 2 decimal number only in case of Octal the base is 8 so we need to take carry when sum of columns are >=8.
Quiz 8
How to do subtraction with Octal numbers.4:34
Let us understand how we can subtract one Octal number from another just using the naive method, we will follow the same procedure as we do while subtracting decimal number here only the change is the base, instead of 10 it is 8, we will need to take borrow of 8 from left column when the digit of subtrahend is less than the minuend.
Quiz 9

Hexadecimal Number System - Converting a Hex number to equivalent decimal.5:50
Learn how numbers can be represented in Hexadecimal system. Also learn how we can convert a Hexadecimal number with a radix point to equivalent decimal number.
Quiz 10
Decimal to Hexadecimal conversion.5:58
Learn how to convert a decimal real number to hexadecimal.
Quiz 11
Addition of Hexadecimal Numbers.3:25
Learn how we can add hexadecimal numbers.
Quiz 12
Subtraction in Hexadecimal.2:43
Learn how to subtract one hexadecimal number from another using the naive method.
Quiz 13

Binary Numbers, how to convert a binary number to equivalent decimal.5:39
Understanding binary numbers, also learn how we can convert a binary number with radix point to equivalent decimal.
Quiz 14
Decimal to binary conversion.4:09
Learn how we can convert a real decimal number to equivalent binary number.
Quiz 15
Let us add binary numbers2:33
Learn how to add binary numbers.
Quiz 16
Subtraction in Binary System using traditional method.2:40
Learn how to subtract one binary number from another using the traditional method.
Quiz 17
Memory Unit5:23
All details of memory units. From bits to Yotta Byte with the interrelationship between them.
Quiz 18

Introduction to signed integer representation.5:47
Introduction to the signed integer representation.
Quiz 19
Understanding the complement.6:39
It is time to understand the complement technique now. It is really the core of signed integer representation.
Quiz 20
Idea of doing subtraction using complements.6:13
Learn how we can do subtraction using the complement, the idea is we will do the subtraction using the addition, aha! sounding odd? Listen to the lecture.
Lets do subtraction of binary numbers using 1s and 2s complement technique.4:24
Learn how we can do the subtraction of binary numbers using 1s and 2s complement technique.
More on 2s complement9:49
Understand the core of 2s complement, how the range of values could be determined in n bits 2s complement system.
On 2s complement.
Range of values in 2s complement representation.4:56
Learn how we can determine the range of values for 2s complement signed integer representation.
2s Complement signed integer range.

Introduction to real number representation.9:13
Let us now understand how real numbers are represented using the IEEE 754 standards.
How decimal reals are converted to IEEE 754 single precision format.6:44
Learn how to convert real decimal number to IEEE 754 single precision format.
How to convert a IEEE 754 single precision binary format to decimal.3:20
Learn how to convert IEEE 754 single precision binary format to decimal.
How biased exponent helps.5:44
Understand the benefit of having the biased exponent.

Requirements

Junior school math skill is required :)
No programming knowledge is required at all.
A pen and paper.
Last but not the least, drink a glass of water before you start listening. :)

Description

The main goal of this course is to teach the basics of Number Theory and how values are represented in the memory of computer. This is very basic knowledge that any programmer/ Computer Science student must posses. This course is to help all those aspiring programmers to build their sound fundamentals with Number Theory.

In order to understand how the information is stored and processed in the memory of computer and other digital systems, students must understand the core concept of Numbers, how they are represented in computer. Good grasp on this topic will make it easier for students to learn programming.

You will learn:

Basic concept of Number Theory.
Standard number systems - Octal, Hexadecimal, Binary.
How to convert number from any of these system to decimal and vice versa.
1s and 2s complement technique. Negative number representation using 2s complement technique.
How subtraction is done using 2s complement in the memory.
Real number representation using IEEE 754 standard (Single and Double precision).

Please do not enrol if you are:

Not interested of doing basic math calculations using pen and paper.
Expecting representations using graphics and animation, I did all the writings on the whiteboard. They are really easy to understand.

Feel free to ask questions in the Q/A section, you will find me always with you during the learning process.

Happy learning!

Who this course is for:

Those who wants to pursue a career in Computer Science or Electronics, particularly as a programmer or research scholar.
Who wants to have a good understanding of how values are represented in memory of computer.
All students who wants to understand different number system.
All students who wants to understand how real numbers are represented in the memory using IEEE 754 standard.

Number Theory for Programmers

What you'll learn

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Course content

Introduction to the course.1 lecture • 3min

Concept of Number and Different Number System.3 lectures • 16min

Octal Number System.6 lectures • 30min

Hexadecimal Number System.4 lectures • 18min

Binary Number System5 lectures • 20min

Signed integer representation (Best understood if done in a single sitting)6 lectures • 38min

Build a number system of your own.1 lecture • 7min

Real number representation - IEEE 7544 lectures • 25min

Requirements

Description

Who this course is for: