How can gates be combined into circuits

As noted in Section 2. First, identify the main operator in the proposition—the one whose value will be computed last. This circuit has two input values, A and B , which are represented by wires coming into the circuit.

The circuit has an output wire that represents the computed value of the proposition. Once the main operator has been identified and represented as a logic gate, you just have to build circuits to compute the input or inputs to that operator. Logic gates process signals which represent true or false.

Other terms used for the true and false states are shown in the table, it is best to be familiar with them all. Capital letters are normally used to make it clear that the term refers to a logic gate. The traditional symbols have distinctive shapes making them easy to recognise, they are widely used in industry and education.

The IEC International Electrotechnical Commission symbols are rectangles with a symbol inside to show the gate function. They are rarely used despite their official status but you may need to know them for an examination. Gates have two or more inputs, except a NOT gate which has only one input. All gates have only one output. Usually the letters A, B, C and so on are used to label inputs, and Q is used to label the output.

On this page the inputs are shown on the left and the output on the right. Some gate symbols have a circle on their output which means that their function includes inverting of the output. It is equivalent to feeding the output through a NOT gate. A truth table is a good way to show the function of a logic gate. It shows the output states for every possible combination of input states. The symbols 0 false and 1 true are usually used in truth tables.

The example truth table shows the inputs and output of an AND gate. There are summary truth tables below showing the output states for all types of 2-input and 3-input gates. These can be helpful if you are trying to select a suitable gate. These summary truth tables below show the output states for all types of 2-input and 3-input gates. Universal Gates. Sum-of-Products Synthesis. SOP Implementation. Boolean Simplification.

Simplified SOP circuit. Pushing Bubbles. Demorganized gate symbols. Circuit Timing. Signal Timing. Non-lenient behavior. Lenient Circuits. Fan-In and Delay.

Systematic Implementation Techniques. Lookup Table Synthesis. Mux-based NAND. Read-only Memories. ROM-based Full Adder.