Presentation on theme: "Ζ Bases Dr Frost Objectives: 1.To appreciate how we can have different number systems using different ‘bases’. 2.To convert numbers from decimal to another."— Presentation transcript:
ζ Bases Dr Frost Objectives: 1.To appreciate how we can have different number systems using different ‘bases’. 2.To convert numbers from decimal to another base. 3.To convert numbers from any base to decimal.
E854 FFBA4D These are all examples of numbers! What connects each group of numbers?
Base The base of a number system is the number of possible values for each digit. Values for each digit BaseName of number system 0 to 910Decimal 0 to 12Binary 0 to F (A=10, B=11,... F=15) 16Hexadecimal ?? ?? ??
Numbers in decimal If we were to write out 2493, what is the value of each digit? = 2493 multiply ? ? ?
Numbers in decimal Now suppose we had a number in base 5 instead. How do we convert it to decimal? = 576 multiply ? ? ?
Numbers in decimal Copy and complete in your book = 11 ? ? = 242 ? ? The small number indicates the base = 51 ? ?
(Switch to ‘I’m a Mayan’ slides)
Exercises Original numberIn base 10 (decimal) Base 2 ? ? ? ? ? ? ?
Converting FROM decimal to other bases Do the opposite! Convert 18 to binary ? = 18 ? ? ? ? ?
Converting FROM decimal to other bases Convert 272 to base ? = 272 ? ? ??
Converting FROM decimal to other bases It can help to write out multiples of your various powers. Below is base 6. Multiples of 6Multiples of 6 2 Multiples of x 1 x 2 x 3 x 4 x 5 Therefore what is 800 is base 6? 3412 ?
Decimal to Hexadecimal The most well-known usage of hexadecimal is to represent colours. Each colour can be composed of red, green and blue light, each of intensity varying between 0 and which can be represented using just 6 digits in hexadecimal, 2 for each of the three colour components. A means 10, B means 11,... F means 15
QQQ Time The number of possible values each digit can have. 1a 1b Because each digit must be between 0 and one less than the base/the digits must be less than the base. 2a 2 2b a = 2, b = 4 ? ? ? ? ? ? ? ? ? ?