Student eLearning project site explaining the numbering systems of Base 16 Hexadecimal, Base 8 Octal and Base 2 Binary. This site provides textual, audio visual and static content that explains the fundamentals of numbering systems.

Introduction

This lesson is a course helping students to understand the fundamentals of converting regular decimal numbers to base numbers; Decimal to Binary, Decimal to Octal and Decimal to Hexadecimal. The lesson is aimed at being a supplemental accompaniment to Computer Science students, IT students or anybody interested in understanding Decimal to Base number conversion.

Users should have an introductory level of knowledge to Computers or IT systems. A user may have experienced the fundamentals of Databases or have an interest in how Internet Protocols work.

Hexadecimal

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Introduction

The Hexadecimal numbering system uses 16 characters to represent values. Hexadecimal uses all the decimal characters (0-9) plus 6 letters (A-F) to represent 16 values.

Uses

Hexadecimal is the future addressing system of the Internet and is widely used as a system to represent colours in multimedia authoring environments.

Conversion

Each hex value is actually a representative value for a decimal equivalent. The hex value of 12516 is a number that represents 3 different values. The table below shows how each hex value is a multiple of 16x to a power.

Hexadecimal to Decimal
Power 163 162 161 160
Decimal 4096 256 16 1
Hex 0 1 2 5

Eg. Calculate the Decimal10 value
(5 * 160)
+
(2 * 161)
+
(1 * 162)
=
29310

The Hexadecimal value 12516 is equal to 29310 decimal. The decimal equivalent is calculated by multiplying each representative value by the hex value as shown in the example above.

 

Octal - 478

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Introduction

Octal is a numbering system based upon using eight digits to represent all values. The range of digits used by the octal system is between 0-7. The numbers 8 & 9 are not included in the octal system.

Conversion

When converting from an Octal base to a Decimal base, the octal values are actually representative of decimal values.

Octal to Decimal
Power 84 83 82 81 80
Decimal 4096 512 64 8 1
Octal 0 0 0 4 7

Using the octal value of 478 each value represents a decimal value which is equal to the formula ( X8 * 8x ) for each value of Octal, in the case of 478 the example below demonstrates how 478 will be converted to 3910

Eg. Calculate the Decimal10 value
(7 * 80)
+
(4 * 81)
=
3910

Binary - 000100102

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Introduction

Binary is the language of electronic communication and is used for addressing the Internet, it is the perfect representation of electronic circuitry that is used to connect computers, networks and their components together. The problem with Binary is that humans find it next to impossible to understand, so it is vital that it is converted into a form that humans do understand, Decimal.

Decimal to Binary

Computer systems use 8-bit Binary code to communicate; a bit being a single digit either One or Zero.
Binary
000100102

The Binary number in the table above is equal to eighteen in the Decimal base. Each bit is representative of a decimal number as shown in the table below. Each decimal number is equivalent to a power of 2:

This table converts a Decimal value to a Binary value.
Power 27 26 25 24 23 22 21 20
Decimal 128 64 32 16 8 4 2 1
Binary 0 0 0 1 0 0 1 0

Calculate

To calculate the value of the Binary number and convert it to Decimal the decimal numbers that are represented by 1’s are added together to give a value of eighteen. The maximum value that an 8 bit binary number can represent is 25510.

This table adds all the decimal values together
  Total
Decimal10 128 64 32 16 8 4 2 1 25510
Binary2 1 1 1 1 1 1 1 1  

12810 + 6410 + 3210 + 1610 + 810 + 410 + 210 + 110 = 25510