Understanding Binary Code and Number Representation in Coding
Explore the world of binary code and number representation in coding through examples like writing numbers in binary, comparing decimal numbers with binary code, and understanding how binary values work. Discover the relation between binary values and decimal numbers in a visual and interactive manner.
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Presentation Transcript
Coding with numbers Launch NSW Department of Education
Writing the number 13 in code Coding with numbers Number 64 32 16 8 4 2 1 Code 1 1 0 1 13 1 1 0 1 What do you notice? What do you think? What do you wonder? 2
Writing the number 20 in code Coding with numbers Number 64 32 16 8 4 2 1 Code 1 0 1 0 0 20 1 0 1 0 0 Can you describe what is happening? 3
An explanation of binary code Coding with numbers Number 64 32 16 8 4 2 1 Code 1 0 1 1 0 1 45 1 0 1 1 0 1 We have just seen the numbers 13, 20 and 45 written using binary code. 4
Comparing decimal numbers with binary code Coding with numbers Binary code Number 64 32 16 8 4 2 1 Code 1 1 0 0 1 0 0 100 1 1 0 0 1 0 0 Decimal number Number 10000 1000 100 10 1 Code 100 100 1 0 0 5
Using binary code Coding with numbers Can you determine the binary code for these numbers? Remember to only use the symbols 0 and 1. Code Number 64 32 16 8 4 2 1 11 18 39 83 6
How the binary values work Coding with numbers Did you notice that the binary values are doubled each time, as they move from right to left? 2 2 2 2 2 2 ? ? 64 32 16 8 4 2 1 What would be the next two values to the left of 64? 7
Writing the binary values in a different form Coding with numbers 256 128 64 32 16 8 4 2 1 What are some things that the numbers in the table have in common? 8
Writing the binary values in index form Coding with numbers Binary value 64 32 16 8 4 2 1 25 26 24 23 22 21 20 Index form What do you notice? What do you think? What do you wonder? 9
Comparing multiplication strategies Coding with numbers Binary value 64 32 16 8 4 2 1 26 24 23 22 21 20 25 Index form Binary values in index form Binary values 22 21= 23 4 2 = 8 What do you notice? What do you think? 10
Investigating multiplication strategies Coding with numbers Binary value 64 32 16 8 4 2 1 25 24 23 22 21 20 26 Index form Binary values Binary values in index form 22 23= 2__ 4 8 = __ __ 25= 26 __ 32 = 64 22 __ = 24 4 __ = 16 21 __ 23= 26 2 4 8 = __ 23 __ = 23 8 1 = __ 11
Investigating multiplication strategies solutions Coding with numbers Binary value 64 32 16 8 4 2 1 25 26 24 23 22 21 20 Index form Binary values Binary values in index form 22 23= 2? 4 8 = ?? ?? 25= 26 ? 32 = 64 22 ??= 24 4 ? = 16 21 ?? 23= 26 2 4 8 = ?? 23 ??= 23 8 1 = ? 12
Comparing division strategies Coding with numbers Binary value 64 32 16 8 4 2 1 26 25 24 23 22 21 20 Index form Binary values in index form Binary values 23 21= 22 8 2 = 4 13
Investigating division strategies Coding with numbers Binary value 64 32 16 8 4 2 1 25 26 24 23 22 21 20 Index form Binary values Binary values in index form 23 22= 2__ 8 4 = __ 26 __ = 25 64 __ = 32 25 22= __ 32 4 = __ __ 20= 23 __ 1 = 8 24 24= __ 16 16 = __ 14
Investigating division strategies solutions Coding with numbers Binary value 64 32 16 8 4 2 1 25 26 24 23 22 21 20 Index form Binary values Binary values in index form 23 22= 2? 8 4 = ? 26 ??= 25 64 ? = 32 25 22= ?3 32 4 = ? ?3 20= 23 ? 1 = 8 24 24= ?? 16 16 = ? 15
