1. Boolean math is the cornerstone of digital communications, whether you are talking computers, PLC, or Cisco Routers on the Internet. ©Emil Decker, 2009

2. Boolean logic, developed by George Boole (1815- 1864), is often used to determination a system’s status or to set or clear specific bits. Boolean logic is simply a way of comparing individual bits. ©Emil Decker, 2009

3. Computers use bits to carry information. Imagine at its lowest level a computer uses electricity to represent data. Electricity can be either on, or off. A system using these two options is quite efficient. ©Emil Decker, 2009

4. To understand boolean math, you must understand the basics of the binary number system. This system is base 2, and there are two options to work with. They are 0 and 1. No digit is zero, and 2 0 is one. Consider these as bits of information. ©Emil Decker, 2009

5. 2 1 is 2 2 2 is 4 2 3 is 8 2 4 is 16 2 5 is 32 2 6 is 64 2 7 is 128 ©Emil Decker, 2009

6. Computers take individual bits, and combine them into strings of 8 to make a byte. This would be 2 8. 2 8 = 256. There would be 256 different options of 1s and 0s in a byte of information. ©Emil Decker, 2009

7. Binary byte = decimal # 00000000 = zero 00000001 = 1 00000010 = 2 00000011 = 3 00100101 = 37 11111111 = 255 ©Emil Decker, 2009

8. Computers can process binary numbers much faster than humans. Electronic components have been created to process these bits and bytes. Logic circuits are built with gates, which compare bits and allow electricity to flow or not. ©Emil Decker, 2009

9. These gates use boolean logic to make their determination. There are really only three basic gates. The AND, OR, & NOT gates. These can be combined to make up to 7 types of gates. A B C C C B A A ©Emil Decker, 2009

10. Let’s see how it works. An AND gate does just what it says. Using a basic logic, one would say that C is the area that is in both A AND B. A B C AND GATE ©Emil Decker, 2009

11. If A and B are the input signals, then C would be the sum of A AND B. Since digital is only a 1, sending a signal”, or a 0, “sending no signal”, C would be a 1 output only if both A and B were 1s A B C AND GATE A B C ©Emil Decker, 2009

12. Boolean logic tables look like this. With no inputs, you get no outputs. With one input, you still get no output. Only when you supply an input on A AND B will you get an output on C. A B C 0 0 0 1 0 0 0 1 0 1 1 1 AND GATE ©Emil Decker, 2009

13. Let’s see how it works. An OR gate does just what it says. Using a basic logic, one would say that C is the area that is in either A OR B. A B C OR GATE ©Emil Decker, 2009

14. If A and B are the input signals, then C would be the sum of A OR B. Again, since digital is only a 1, sending a signal”, or a 0, “sending no signal”, C would be a 1 output if A or B were 1s A B C OR GATE A B C ©Emil Decker, 2009

15. An OR Boolean logic table looks like this. With no inputs, you get no outputs. With an input on either leg, you get an output. When you supply an input on A OR B will you get an output on C. A B C 0 0 0 1 0 1 0 1 1 1 1 1 OR GATE ©Emil Decker, 2009

16. A NOT gate is also called an Inverse gate. Whatever signal is presented on the input, the opposite, or inverse in given on the output. NOT GATE A C ©Emil Decker, 2009

17. A NOT Boolean logic table looks like this. With no input, you get an output. When you supply an input on A you will NOT get an output on C. A C 0 1 1 0 NOT GATE ©Emil Decker, 2009

18. By combining a NOT gate, (often shown as a circle), with an AND gate will create a NAND gate. A NOT combined with an OR gate gives you a NOR. Their logic tables work like this. A B C C A B ©Emil Decker, 2009

19. Your NAND table works just like the AND table, but the final outcome is reversed. A B C 0 0 1 1 0 1 0 1 1 1 1 0 NAND GATE C ©Emil Decker, 2009

20. Your NOR table works just like the OR table, but the final outcome is reversed. A B C 0 0 1 1 0 0 0 1 0 1 1 0 NOR GATE A B C ©Emil Decker, 2009