## 1: Numbering Systems and Conversions

TOPIC 1: Numbering Systems

In digital control systems we will need to understand the ways in which these systems represent numbers. We traditionally use the decimal numbering system but computers use binary and when we program and try to understand what the computing system is doing we use hexadecimal and octal systems. The systems work the same but use a different number of characters to represent numbers.

Decimal Numbering System Audio

Octal Numbering System Audio

Binary Numbering System Audio

Hexadecimal Numbering System Audio

TOPIC 2: Converting Between Numbering Systems

Converting from any numbering system to decimal is almost identical so we will discuss those first.

Converting from Binary to Decimal Audio

Converting from Octal to Decimal Audio

Converting from Hexadecimal to Decimal Audio

And likewise, converting from decimal to any other base is almost identical and we will discuss them as a group.

Converting from Decimal to Binary Audio

Converting from Decimal to Octal Audio

Converting from Decimal to Hexadecimal Audio

And finally, the remaining six possibilities are Hexidecimal to Binary and back, Octal to Binary and back, and Hexidecimal to Octal and back.

Converting from Hexadecimal to Binary and reverse Audio

Converting from Octal to Binary and reverse Audio

Converting from Octal to Hexadecimal and reverse Audio

One last issue that will benefit from a short focus. There are two positions in a number that are often given names. These are the Most Significant Digit (MSD) or specifically the Most Significant Bit (MSB) in binary and the Least Significant Digit (LSD) or specifically the Least Significant Bit (LSB). The names are used commonly in the binary system. The MSB is the bit farthest to the left as it has the most value in the number and the LSB is the number furthest to the right because it has the least value in the number. For example the binary number (MSB)01001001(LSB) represents 73. If the LSB changes the decimal value changes by 1. If the MSB changes the decimal value changes by 128.

You should now be prepared to begin the assessment game. If you hit a score of 2000 you are guaranteed an 80%, after that you are competing with your peers. The highest score gets 100%. To determine other grades (if your score is greater than 2000) I will take 80+ (your score-2000) x (20/((the highest score) – 2000)). If your score is less than 2000 your grade will be (80/2000)x(your score).

This game does not really come to an end so to submit, take a screen capture of the game when you decide to stop and email it to me in a word document.

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