Following corrections from others and more questions I have edited my original reply.
Binary, Integer and Real are the types of number that you will normally use in a PLC.
Binary can only have two values 0 or 1, Off or On.
Integer numbers don't have a decimal point and so can only be whole numbers.
Real or Float numbers do have a decimal point and so can be numbers like 3.142.
Bit, Byte, Word, and Double Word are the things that you store the numbers in.
So a bit will store a Binary number.
A Byte will store a small Integer number.
A Word will store a larger Integer number.
A Double Word will store either a Real number or a large Integer number.
How to choose an Integer or Real
It can be tempting to use Real numbers all the time because it can be any value you want with or without numbers after the decimal point. But Real numbers always need the storage space of a Double Word and Real calculations usually take longer than Integer ones. Also Real numbers are less accurate than Integer ones, for instance get your calculator and divide 1 by 3 and you get 0.33333 (may be more or less 3s depending on the screen size). But that isn't the true value, you would have to have an infinite number of 3s to truly represent 1/3. If you now multiply 0.33333 by 3 you get 0.99999 which is nearly the 1 we started with, but not quiet, it is an inaccurate 1. So use Real where you need to but use Integer wherever you can.
Byte, Word Or Double Word
Real numbers always use a Double Word so for them you have no choice but Integers can use any one of the three, and it is all about size. If you were asked to move two gallons of water would you choose to use a 5 gallon bucket or a 60 gallon drum, the bucket is more appropriate because that is the best fit. Same when it comes to Integers if you have a small Integer and any maths you do on it will result in a small Integer then use a Byte or Word size of storage. If you have a large Integer or any maths you do will result in a large Integer then use a Double Word size. There are exceptions to this rule, if most of the time a Word length will be OK but occasionally you need Double Word then you can convert from Word to Double and back again. But generally stick to the rule and you won't go wrong. And yet another exception, HMIs don't always like Bytes, so check what values your HMI can use.
What vaules can a Byte, Word and Double Word hold
This totally depends on your PLC and how many bits it uses in its calculations but listed below are the current norms for 16 bit system:
A Byte is 8 bits and storing an Integer can hold 255 without a + or -, or -128 to +127.
A Word is 16 bits and storing an Integer can hold 65535 without a + or -, or -32768 to +32767.
A Double Word is 32 bits and storing an Integer can hold 4294967295 without a + or -, or -2147483648 to +2147483647. Storing a Float/Real it can hold (-1.175495E-38 to -3.402823E+38 negative) to (+1.175495E-38 to +3.402823E+38 positive). A float/real value uses some of the 32 bits to hold the number before the E and some of the 32 bits to hold the number after the E. This is why if you view an integer value as a float/real or a float/real as an integer you will get a rubbish answer.
For an explanation of the E number system see below. The values given are for a Siemens S7-200 range PLC, check the manual of your PLC to be certain that they are the same.
If you want to see how Bits and Integer numbers are related start calculator in Windows and choose scientific from the View menu. Click on Bin and then enter a value of 16 1s. Click on Dec and it will convert that value to a Decimal Integer.
If you want to see the E notation in use then again use the Windows calculator and choose scientific from the View menu. Enter 5.27 then press the Exp button and enter 3, the result is 5270. So to translate 5.27E+3 to normal notation you just move the decimal point 3 places to the right. To translate 5.27E-3 you would move the decimal point 3 places to the left, 0.00527. (To use the negative values with the Windows calculator enter a value and then press the +/- key).
Relationship between Bits, Bytes, Words and Double Words
The relationship varies between PLCs, for instance for the Siemens S7-200 range the bits use a totally separate section of memory from the rest of the numbers. The picture below shows the relationships for a Moeller Easy Smart relay and a Siemens S7-200, check your PLC manual to be certain that it is the same.
Below for the Moeller: if you set M15 to 1 then MB01 would be 0, MB02 would be 64, MW01 would be 16384, MD01 would be 16384. Enter the values on the calculator to check.
Bryan
