1.5 Math for a Digital Age
1.5.3 Boolean logic gates

Computers are built from various types of electronic circuits. These circuits depend on what are called AND, OR, NOT, and NOR logic "gates". These gates are characterized by how they respond to input signals. Figures - show logic gates with two inputs. The "x" and "y" represent inputs, and the "f" represents output. Think of 0 as representing "off" and 1 as representing "on".

There are only three primary logic functions. They are AND, OR, and NOT. An OR gate acts if either input is on, the output is on. The AND gate acts if either input is off, the output is off. A NOT gate acts if the input is on, the output is off, and vice versa.

The NOR gate is a combination of the OR and NOT gates and should not be presented as a primary gate. A NOR gate acts if either input is on, the output is off.

These functions are illustrated in the tables for reference. All the other functions can be derived from these.

0 OR 0 is 0 0 AND 0 is 0 0 NOR 0 is 1 NOT 0 is 1
0 OR 1 is 1 0 AND 1 is 0 0 NOR 1 is 0 NOT 1 is 0
1 OR 0 is 1 1 AND 0 is 0 1 NOR 0 is 0  
1 OR 1 is 1 1 AND 1 is 1 1 NOR 1 is 0  

It helps to look at the "truth tables" in Figure to represent these statements in a compact form. Other logic gate combinations or extensions such as XOR, NAND, and so on, are beyond the scope of this course. Information about these can be obtained from more advanced literature including web resources such as http://www.whatis.com.

Lab Activity  (PDF, 13 KB)
  In this lab, students will be introduced to the AND, OR, NOR, and NOT Boolean operations. Students will also be able to calculate the output of combinations of Boolean operations based on input.