Is this correct?

BOOL: 0= Cleared 1= Set
SINT: -128 to 127
INT: -32,768 to 32,767
DINT: -2,147,483,648 to 2,147,483,647
REAL: -3.402823e^38 to - 1.1754944e^-38 and 1.1754944e^-38 to 3.402823e^38

These number values to the right of the Data types is information just for humans to read. They can be displayed in these ways: Binary, decimal, hexadecimal, octal, exponential, and float, depending on what your seeking. Those numbers are not of any purpose for the PLC. For the PLC to code those values for us, it is done through a binary format. They can be coded in these ways: BOOL, SINT, INT, DINT, and REAL. I want to know if this is right or wrong.

This looks correct.
Most references will have signed and unsigned values separate. You have to check each manufacture of PLC to determine if they have all of these values or a combination of just certain ones.
http://accautomation.ca/what-everybody-ought-to-know-about-plc-programmable-logic-controller-numbering-systems/

Regards,
Garry
http://www.accautomation.ca

Okay, thanks.

What are you really trying to ask?
And there is more to the Real type than just the ranges.

I just entered the PLC programming world, and was given a few things to review. I wanted to know the functions of data types, what information they hold, and how they could be displayed. I was looking through some programs on RSL5000 and become confused with BOOL, SINT, INT, DINT, REAL and binary, decimal, hexadecimal, octal, exponential, and float.