🔢 Number Systems
03 Nov 2016Do Now (in Classroom)
The letter A is represented by 65 in ASCII, the protocol used by most computers for text encoding.
American Standard Code for Information Interchange, a set of digital codes representing letters, numerals, and other symbols, widely used as a standard format in the transfer of text between computers.
Deep inside your computer, that 65 is sent in binary. What is 65 in binary?
🎯 Learning Targets
I can use number bases, including binary, decimal, and hexadecimal, to represent and investigate digital data.
I can explain why hexadecimal is used to represent digital data.
Review decimal & binary
Let’s write 15:
Decimal:
In decimal, we have 10 symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
15 in decimal:
| 1000 | 100 | 10 | 1 |
|---|---|---|---|
| 1 | 5 |
Binary
In binary, we have 2 symbols: 0, 1
15 in binary:
| 8 | 4 | 2 | 1 |
|---|---|---|---|
| 1 | 1 | 1 | 1 |
Binary numbers start to get very long, very quickly.
Hexawhatnow?
Hexadecimal - base 16
Hexadecimal
In hexadecimal, we have 16 symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, a, b ,c, d, e, f
Wait, what?
15 in hexadecimal is f.
| 4096 | 256 | 16 | 1 |
|---|---|---|---|
| f |
Notice!
- How many
bitsdoes it take to write 15 in decimal, binary, and hexadecimal? - Hex looks just like decimal…until we try to write 16:
Hexadecimal
| 4096 | 256 | 16 | 1 |
|---|---|---|---|
| 1 | 0 |
Where have we seen hex before?
#E32173
That’s my favorite pink, Razzmatazz. Colors can be represented by mixing red, green, and blue. How much RGB is Razzmatazz?
It’s 227 red, 33 g, and 115 blue. How do I know that?
| Razzmatazz | R | G | B |
|---|---|---|---|
| Hex | E3 | 21 | 73 |
| Decimal | 227 | 33 | 115 |