# 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 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.

1001100101 11010001 96E854 FFBA4D 000000 12958 23 8409284 These are all examples of numbers! What connects each group of numbers? 10 942

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? 2 4 9 3 1000 100 10 1 2000 +400 +90 + 3 = 2493 multiply ? ? ?

Numbers in decimal Now suppose we had a number in base 5 instead. How do we convert it to decimal? 4 3 0 1 125 25 5 1 500 + 75 + 0 + 1 = 576 multiply ? ? ?

Numbers in decimal Copy and complete in your book. 1 0 1 1 2 8 4 2 1 8 + 0 + 2 + 1 = 11 ? ? 3 3 0 2 4 64 16 4 1 192 + 48 + 0 + 2 = 242 ? ? The small number indicates the base. 1 2 2 0 3 27 9 3 1 27 + 18 + 6 + 0 = 51 ? ?

(Switch to ‘I’m a Mayan’ slides)

Exercises Original numberIn base 10 (decimal) 1101 2 13 111 2 7 110011 2 51 1022 3 35 734 8 476 234 5 69 530 6 198 Base 2 ? ? ? ? ? ? ?

Converting FROM decimal to other bases Do the opposite! Convert 18 to binary. 1 0 0 1 0 2 16 8 4 2 1 ? 16 + 0 + 0 + 2 + 0 = 18 ? ? ? ? ?

Converting FROM decimal to other bases Convert 272 to base 5. 2 0 4 2 5 125 25 5 1 ? 250+ 0 + 20+ 2= 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 6 3 6 12 18 24 30 36 72 108 144 180 216 432 648 864 1080 x 1 x 2 x 3 x 4 x 5 Therefore what is 800 is base 6? 3412 ?

Exercises DecimalBinaryBase 6 3113 810012 10101014 771001101205 1021100110250 1051101001253 13651010101010110153 ? ? ? ? ? ? ? ? ? ? ? ? ? ?

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 255....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

02550 000 REDGREENBLUE 255 0 75172198 2551280 ??? ??? ??? ??? HEXADECIMAL FF, FF, FF 00, 00, 00 00, FF, 00 FF, FF, 00 4B, AC, C6 FF, 80, 00 ??? ? ? ? ? ? 0: 0 1: 16 2: 32 3: 48 4: 64 5: 80 6: 96 7: 112 8: 128 9: 144 A: 160 B: 176 C: 192 D: 208 E: 224 F: 240 Multiples of 16:

Exercises Provided worksheet.

Adding in other bases 1 0 0 1 + 1 1 0 1

Adding in other bases 1 0 1 0 + 1 1 0 1 1

Multiplying in other bases 1 0 1 0 x 1 0 1

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 178 3 551 4 5 6 7 8 3900 11011 240 100100 a = 2, b = 4 ? ? ? ? ? ? ? ? ? ?

Download ppt "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."

Similar presentations