Section 6 Primitive Data Types

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

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)

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, -15.25, -0.2

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)

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

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

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

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

Binary to denary and vice versa Convert the following binary numbers into denary 00010000 00001111 00010001 00000000 10111001 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?

Representing positive integers in binary – Answers Convert the following binary numbers into denary 00010000 = 16 00001111 = 15 00010001 = 17 00000000 = 0 10111001 = 185 Convert the following denary numbers into binary 140 = 10001100 68 = 01000100 201 = 11001001 What is the largest denary value that can be stored in an 8-bit binary integer? 255

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

+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 4 2nd four bits equal a value of 14 1st hexadecimal value is 4 2nd hexadecimal value is E Denary +78 = 4E in hexadecimal

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 128+64+32+16+2 = 242 So F2 = 242

Convert Denary to Hex Sheet on intranet