Beginner's Guide to Coding and Data

Decoding Numerals and Numbers

Let's kick off this journey with a fascinating experiment. Picture the number 12 in your mind. Now, what did you really see? We have both good news and bad news about that.

In this exploration, we will focus on several key ideas:

1. The distinction between numbers and numerals
2. Types of numeral systems
3. Positional numeral systems and their bases

Numbers vs Numerals

We've all encountered numbers and numerals, but do we know the difference? A number is an abstract concept, while a numeral is the symbolic representation of that concept.

• Numbers are abstract
• Numerals are concrete representations

Types of Numeral Systems

There are various ways to represent numbers—tallies, text, or even Roman numerals. But these are all examples of numerals. They take an abstract concept and make it concrete.

# Different ways to represent the number 12
twelve_in_text = "twelve"
twelve_in_tallies = "||||||||||||"
twelve_in_roman = "XII"
twelve_in_decimal = 12

The Power of Positional Systems

We soon realize that using tally marks is cumbersome for large numbers. That's when positional numeral systems like binary and decimal come in handy. These systems have a base and allow us to easily perform arithmetic.

# Binary and Decimal representation of the number 12
twelve_in_binary = "1100"
twelve_in_decimal = "12"

Exploring the Bases

When we stumble upon a list of numeral systems, we'll find that each has a base. The most commonly used are base 2 (binary) for digital computing and base 10 (decimal) for everyday tasks. But there's a whole array of other bases out there.

Check out the following resource to see other numeral systems and their bases:

1. Open a browser
2. Search for: List of numeral systems Wikipedia
3. Explore the Usage column for each system

So stay tuned and let us know if you have any questions in the comments. We'll dive deeper into this topic in our next lesson!