Easy Binary, Hexadecimal, and Octal Math Conversion

Name: Easy Binary, Hexadecimal, and Octal Math Conversion
Rating: 4.7 (30 reviews)

The easiest way to convert from Hex<=>Binary, Binary<=>Octal, Decimal<=>Octal, and more!

Created byW S

Last updated 10/2014

English

English [Auto],

What you'll learn

Convert Decimal<=>Binary
Convert Decimal<=>Hex
Convert Hex<=>Binary
Convert Hex<=>Octal
Convert Decimal<=>Octal
Fractional conversion from Decimal<=>Binary

Course content

1 section • 8 lectures • 36m total length

Counting in base-n3:58
master counting in base-n using the correct symbols and wrap digits to the next column; base-16 uses 0–9 and a–f.
Converting Decimal to Binary, and vice versa5:51
Learn to convert decimal to binary and back using powers of two, with examples like 10 to 1010 and 255 to 11111111_2, and decode 101101_2 to 45.
Converting Binary to Hex, and vice versa4:33
Master binary to hexadecimal conversions by grouping four bits into a nibble and converting nibble to hex digit, and vice versa. Memorize nibble patterns and use leading zeros when needed.
Converting Decimal to Hex, and vice versa4:02
Convert decimal to hex by converting to binary first, then map each nibble to a hex digit; convert hex back to decimal by summing digits times powers of 16.
Converting Binary to Octal, and vice versa1:35
Master converting between binary and octal, using the three binary digits per octal digit rule and leading zeros to translate bits and digits in both directions.
Converting Decimal to Octal, and vice versa4:05
Learn how to convert decimal to octal and back by converting decimal to binary first, then grouping binary digits in threes to map to octal digits, with examples.
Fractional Decimal to Fractional Binary5:38
Convert fractional decimal numbers to binary by subtracting descending powers of two and using binary fractions for the remainder. Explore converting fractional binary back to decimal to verify accuracy.
Review: Binary as an intermediate step6:55
Convert decimal to binary, then translate to hexadecimal or octal with four- or three-bit groups. Learn a left-to-right method using powers of two to build and read the binary.

Requirements

Pen and paper
Firm grasp of regular addition, subtraction and multiplication

Description

Number systems are a common math and computer science topic. This course is about mastering conversion between 4 common number systems: Decimal, Binary, Octal and Hexadecimal.

Number System Conversion The Easy Way!

Convert Decimal<=>Binary
Convert Decimal<=>Hex
Convert Hex<=>Binary
Convert Hex<=>Octal
Convert Decimal<=>Octal
Fractional conversion from Decimal<=>Binary

In this course, I teach and show through example how to easily convert between Binary (base 2), Octal (base 8), Decimal (base 10), and Hexadecimal (base 16). We start by counting in base-n, and get a feel for what counting in a base-n system really means. You will understand how a base-n system only has n digits to count with (for example, in Decimal there are only 10 digits), and how we can reach higher numbers after using up those 10 digits.

Through these lectures, we explore the special relationship between Hexadecimal and Binary (a hex digit is really four binary digits), and Octal and Binary (an octal digit is really 3 binary digits). Binary is really the star of this course. We spend some time in the course exploring these relationships between Octal and Binary and Hexadecimal and Binary. In the Hexadecimal to Octal lecture, I show how the computation can be made super easy by using Binary as an intermediate conversion step. You’ll wonder how you managed these conversions without this technique! You probably won’t learn an easier method!

We also cover conversion from fractional Decimal numbers to fractional Binary. You will probably find it surprisingly easy!

Conversions between number systems almost always show up on computer science tests. You want to be able to breeze through these conversions quickly, easily, and correctly. If you enjoy math, you’ll find this course a nice leisurely exercise. After this course, you will walk away from this course a master of number system conversion. You will feel very comfortable converting between each of Decimal, Hex, Octal and Binary.

Who this course is for:

You want to learn to do decimal <=> hexadecimal and decimal <=> octal conversions in a fast and efficient way
You should take this course if you want to learn to work with the Binary number system in a very deep and useful way
You can also take this course if you like to have fun with math