Binary Numeral System (Number System) Complete Course | Decimal ↔ Binary | 1's & 2's Complement

Learn the Binary Numeral System (Binary Number System) from scratch in this complete course. In this tutorial, you will understand how numbers are represented in binary, why computers use binary, and how to convert between decimal and binary numbers.

Topics Covered:
✔ What is the Binary Numeral System?
✔ Binary Digits (0 and 1)
✔ Binary Place Values
✔ Decimal to Binary Conversion
✔ Binary to Decimal Conversion
✔ Representation of Positive and Negative Numbers
✔ 1's Complement
✔ 2's Complement
✔ Binary Number Representation in Computers

This Binary Numeral System Complete Course is suitable for beginners, computer science students, engineering students, digital electronics learners, and anyone interested in understanding binary numbers and binary representation.

Keywords:
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chapters:

00:00 - Introduction & Recap of Decimal System
00:29 - What is the Binary Numeral System? (Base & Digits)
01:06 - Practical Applications: Digital Electronics & Processors
02:09 - Binary States Explained: High/Low Voltage & On/Off
03:43 - Why is the Base of Binary System 2?
04:18 - Binary as a Positional / Place-Value System
05:55 - How Initial Binary Numbers are Formed (The Concept of Grouping)
07:24 - Writing Numbers 1, 2, and 3 in Base-2
08:22 - The Role of 0 as a Place Holder
11:00 - Representing Number 4 (Higher-Level Grouping)
13:21 - Quick Counting Guide from 5 to 10 in Binary
15:37 - Introduction to Conversion Methods
16:48 - Decimal to Binary: Converting Whole Numbers (Successive Division)
18:56 - Step-by-Step Example: Converting Decimal 25
19:54 - Decimal to Binary: Converting Fractional Parts (Successive Multiplication)
21:32 - Step-by-Step Example: Converting Decimal 0.25
23:11 - Combining Integral and Fractional Parts (25.25)
23:36 - Handling Infinite Repeating Fractions (Example: 0.1)
27:38 - Truncation vs. Rounding Off in Binary Numbers
30:51 - The Rounding Rule Based on System Base Half-Value
32:35 - Binary Carry and Rounding Examples
34:32 - Binary to Decimal Conversion: Whole Numbers (Powers of 2)
40:33 - Step-by-Step Example: Converting Binary 101 to Decimal
41:27 - Binary to Decimal Conversion: Fractional Parts (Negative Powers of 2)
42:25 - Step-by-Step Example: Converting Binary 0.101 to Decimal
44:10 - Signed vs. Unsigned Numbers in Computing
47:26 - The Most Significant Bit (MSB) as a Sign Indicator
51:14 - Calculating Range of Signed Numbers (n-Bit System Formula)
54:40 - Comparing 4-Bit and 8-Bit Signed Data Ranges
55:52 - What is 1's Complement? (Inverting Bits for Negative Numbers)
57:40 - The Fatal Flaw of 1's Complement: The Duplicate Zero Problem
59:58 - Introduction to 2's Complement
01:01:12 - How 2's Complement Solves the Duplicate Zero Issue
01:02:19 - Step-by-Step Example: Finding -5 Using 2's Complement
01:03:41 - Reversing 2's Complement Back to Decimal
01:04:56 - Summary & Teaser for Next Class (Octal, Hexadecimal & Roman)
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