The logic diagram representation is shown below. A logic system has 3 inputs and therefore 8 possible states. What symbol is used to represent the NOT gate when the line over the letter is not convenient to use?ģ. How many possible states exist in this system?Ģ. You should now be prepared to answer the following questions. The easiest way to accomplish this is to first convert the truth table to a boolean expression and then to a logic diagram. It’s best to begin with an example.Īudio Audio Audio Audio TOPIC 9: Converting a Truth Table to a Logic Diagram Inside any parentheses we will look for more parentheses and then NOTs, then ANDs, then ORs.

We will first look for bracketed quantities or something in parentheses. In order to complete this conversion we will progress through the order of operations. Below is the order of operations used in this conversion. TOPIC 8: Converting Boolean Expressions to Logic DiagramsĬonverting boolean expressions to logic diagrams is the most challenging conversion on this page because it requires a very good understanding of order of operation. There are two methods for converting truth tables to boolean expressions. TOPIC 7: Converting Truth Tables to Boolean Expressions The fact that the result simplifies to the XOR is merely coincidental. The following is the resulting boolean expression of each of the gates.Īnd here is an example of the process being carried out. To convert from a logic circuit diagram to a boolean expression we start by listing our inputs at the correct place and process the inputs through the gates, one gate at a time, writing the result at each gate’s output. TOPIC 6: Converting Logic Circuit Diagrams to Boolean Expressions

(Click the image if it isn’t changing) Below are the results of the conversion in truth table form. Study it carefully for an extended period of time, it is an animated image and the inputs and output will change every few seconds. Below is a logic circuit diagram with the input values. The final output value for each state is then listed in the truth table next to the value of each input. This conversion is accomplished by selecting each state (or combination of inputs) one at a time, replacing the inputs with their respective values and figuring the value of each point through the circuit until the output is reached. TOPIC 5: Converting from a Logic Circuit Diagram to a Truth Table This concept will also become clearer when we cover converting from and to the boolean expression below. In fact, it represents the same logic as the example logic circuit diagram above. Care should be used so that you understand which method is being used!īelow is an example boolean expression.

Note: Sometimes when the ! is used to represent the NOT it is used before the letter and sometimes it is used after the letter. There are a few symbols that you’ll recognize but need to redefine. The interpretation of this will become clear in the following sections.īoolean Algebra can be used to write a logic expression in equation form. An example below shows a logic diagram with three inputs (A, B, and C) and one output (Y). (Audio)Ī logic diagram uses the pictoral description of logic gates in combination to represent a logic expression. For example with three inputs there are 2^3=8 possible combination of inputs. There are 2 to the power n possible states (or combination of inputs). The list of all possible inputs are arranged in columns on the left and the resulting outputs are listed in columns on the right. We will discuss each herein and demonstrate ways to convert between them.Ī truth table is a chart of 1s and 0s arranged to indicate the results (or outputs) of all possible inputs.

There are three common ways in which to represent logic.

Logic no input source selected