1. Section 6 Primitive Data Types

2. Lesson Objectives Understand why we need data types
Recognise the main data types used
Know how to convert denary into binary using positive integers
Know how to convert binary into denary using positive integers
Converting between binary, hexadecimal and denary

3. Why we need data types
Different types of data are stored and processed in different ways.
Need to tell computer what type of data it is so it processes it and stores it correctly
What ever the data type – it is stored in the computer as binary base 2 (0’s and 1’s)

4. Data types Type Description Example Character / Char
Single letter, digit, symbol (typically using ASCII), control code
D, d, 9, %, NULL
String
A string of alphanumeric characters enclosed in quotes
“Hello”, “job”, “£20.99”
Boolean
One of two values
True or false
Integer
Whole number values with no decimal part (signed or unsigned)
0, -12, 123, 22
Real / floating point
Numbers with decimal or fractional parts (signed or unsigned)
25.3, , -0.2

5. Number bases Decimal (denary) – 0-9 = Base 10
Binary – 0 and 1 = Base 2
Hexadecimal – 0-9 and A-F = Base 16
These can be written as a subscript:
1110 =11 in denary
112 = binary value
1116 = hexadecimal value (17 in denary)

6. Representing positive integers in binary
First lets look at our denary system
The denary number weighting line multiplies by 10 each time it moves to the left
Thousands
Hundreds
Tens
Units
x1000
x100
x10 x1
So the number 276 is stored as
Thousands
Hundreds
Tens
Units 2 7 6

7. Representing positive integers in binary
With binary – base 2 number system
The numbers weighting line is multiplied by 2 every time we move to the left
128 64 32 16 8 4 2 1
So every time we move to the left we are doubling

8. Representing positive integers in binary
So how would you fit 25 into binary
How many 128 can you fit into 25
How many 64 can you fit into 25
How many 32 can you fit into 25
How many 16 can you fit into 25
25 – 16 = 9
How many 8 can you fit into 9
9 – 8 = 1
How many 4 can you fit into 1
How many 2 can you fit into 1
How many 1 can you fit into 1
1 – 1 = 0
128 64 32 16 8 4 2 1 1 1 1

9. Representing positive integers in binary
So the denary number 25 in binary is:
128 64 32 16 8 4 2 1
This can be confirmed by adding up the weight of the columns that have 1’s in…….. 16 8 1 25

10. Binary to denary and vice versa
Convert the following binary numbers into denary
Convert the following denary numbers into binary
140 68
201
What is the largest denary value that can be stored in an 8-bit binary integer?

11. Representing positive integers in binary – Answers
Convert the following binary numbers into denary
= 16
= 15
= 17
= 0
= 185
Convert the following denary numbers into binary
140 =
68 =
201 =
What is the largest denary value that can be stored in an 8-bit binary integer? 255

12. Why is the Hex system used??
Hexadecimal
Why is the Hex system used??
10000 16 10

13. +78 converted in hexadecimal - First convert into binary
Converting denary into hexadecimal
+78 converted in hexadecimal - First convert into binary
128 64 32 16 8 4 2 1
Then group in sets of four and change weighting line 8 4 2 1 8 4 2 1
1st four bits equal a value of nd four bits equal a value of 14
1st hexadecimal value is nd hexadecimal value is E
Denary = 4E in hexadecimal

14. Converting hexadecimal into denary
F2 as a hexadecimal number Each number/letter represents the value of four bits
F equals a total of 15
2 equals a total of 2 8 4 2 1 8 4 2 1
Change our weighting line back to represent a binary number
128 64 32 16 8 4 2 1
Add = So F2 = 242

15. Convert Denary to Hex
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