Octal - 3056 Hexadecimal 37AD Decimal - 32767 Binary ... 13 HNC Unit 22 LO2_3 PLC Number...

LO2.3 Number systems used by PLCs

Binary - 1010100011

Hexadecimal – 37AD

Decimal - 32767

Octal - 3056

LO2.3 Number systems used by PLCs - Assignment

Take the following 16 bit binary number 1100100011000011 and show how you would convert it to Decimal, Octal and Hex. LO2.3

We can base our number systems on any number. For example we base our monetary system on 10. Decimal, Binary, Octal and Hex are used by computer people and in the PLC world, so that’s three we need to learn about. So how do Number Bases work?


The column heading for Decimal (base 10) numbers are: 10000 1000 100 10 1 These are from: 104 103 102 101 100 So 3456 is 104 103 102 101 100 0 3 4 5 6


So 3456 is 104 103 102 101 100 0 3 4 5 6 This means: 3* 103 = 3*1000 = 3000 4* 102 = 4* 100 = 400 5* 101 = 5* 10 = 50 6* 100 = 6 * 1 = 6


Now humans can handle base ten. But computers can only deal with things being on or off. So we want some way of representing a number bigger than one, as a series of 1’s and 0’s. How many different states can a decimal digit have?


Now humans can handle base ten. But computers can only deal with things being on or off So we want some way of representing a number bigger than one as a series of 1’s and 0’s. How many different states can a decimal digit have? 10 (that is 0 to 9) How many different states can a binary bit have?


Now humans can handle base ten. But computers can only deal with things being on or off So we want some way of representing a number bigger than one as a series of 1’s and 0’s. How many different states can a decimal digit have? 10 (that is 0 to 9) How many different states can a binary bit have? 2 (that is 0 or 1)


The column headings for decimal are, as we said: How many different states can a binary bit have? 2 (that is 0 or 1) So what are the column headings for binary?


104 103 102 101 100

10000 1000 100 10 1

Binary column headings are


24 23 22 21 20

16 8 4 2 1

So if for a Binary number we have:

24 23 22 21 20

1 0 0 1 1

What number is this? Well it’s 100112

But how do we convert that to decimal?


24 23 22 21 20

1 0 0 1 1

24 = 2*2*2*2 = 16 21 = 2 20 = 1 100112 = 1910


Exercise 2 Create the column headings for numbers at base 16 If I have the number 175 how does that convert to Hex? What problem do you have? Can you think of a solution?



Problem – With base 16 how can we represent the numbers 10 to 15 with one digit each?

Solution – We use letters for 10, 11, 12, 13, 14 and 15

So the numbers go 1,2,3,4,5,6,7,8,9,A,B,C,D,E,F So 175 decimal is AF in hex i.e. (10*16) +15

Conversion of Binary to Hex – We could convert to decimal and then to Hex ..... Exercise 4


Break the number into fours from the right. 1101 0110 0001 1011 And make a Hex digit from each group of four “four bit” binary groups. 8 4 2 1 1 1 0 1 so this is worth? 13 and in Hex that is D Exercise 4: Convert it and see what you get as an answer


Let’s convert the number below to Octal (base 8). 1101011000011011


Let’s convert the number below to Octal (base 8). 1101011000011011 In base 8 what is the biggest value digit you can have? ........... And how many binary bits do you need to represent it? ........... So we can split the big binary number into blocks of .......... each of which represents an octal digit.


Let’s convert the number below to Octal (base 8). 1101011000011011 Make an Octal digit from each group of 6 “three bit” binary groups starting on the right. 4 2 1 1 0 1 so this is worth? 5 Exercise 4: Convert the binary number above to octal


Let’s convert the number below to Octal (base 8)


1 5 3 0 3 3

85 84 83 82 81 80

1 101 011 000 011 011

32767 4096 512 64 8 1

= 1530338

Octal - 3056 Hexadecimal 37AD Decimal - 32767 Binary ... 13 HNC Unit 22 LO2_3 PLC Number...

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