1. Unit 18: Computational Thinking
Number systems

2. Bits and bytes A 4 bit number looks like this:
1 bit = a binary digit
A 4 bit number looks like this:
1001
How many possible different 4 bit numbers are there?
Hint: work out the minimum and maximum in decimal
0000
1111

3. Bits and bytes A 4 bit number has 16 different possible values
It has 2*2*2*2 or 2 to the power 4 combinations
2*2*2*2 = 16
A byte has 8 bits
How many different possible combinations?

4. Bytes 2 to the power 8 2*2*2*2*2*2*2*2 = 256 Minimum = 00000000
Maximum =
Writing bytes in binary is:
Tedious
Error-prone

5. Hexadecimal to the rescue!
Makes life easier
Now count to 15 using a single digit
0, 1, 2, 3, 4, 5, 6, 7, 8, 9
That was easy – just like decimal!
What about 10 and up?
10 = A 14= E
11= B 15= F
12= C 16= 10 (We now need
13= D an extra place value)

6. Hexadecimal

7. Hexadecimal So instead of 4 bits we have 1 hexadecimal digit
8 bits = 2 4 bit sections
Convert each to hex
Now have 256 = 1 byte = 2 hex digits

8. Conversion to hex Start with decimal number e.g. 36 Convert to binary
= 32 (2*2*2*2*2)+4(2*2)
= as binary
Split into 2 4-bit sections
0010 and 0100 (written as )
Convert each 4-bit section to hex
0010 = 2, 0100 = 4
36 decimal = binary = 24 hex

9. Try it yourself
Convert the following decimal numbers to binary and then to hexadecimal. 34 63
127
244 57 98
Convert the following hexadecimal numbers to binary and then to decimal CC 33 AF 1F 8E FE

10. What about letters then?
ASCII
American Standard Code for Information Interchange
ITF