![]() This cookie is set by GDPR Cookie Consent plugin. ![]() The cookie is used to store the user consent for the cookies in the category "Other. The cookies is used to store the user consent for the cookies in the category "Necessary". The cookie is set by GDPR cookie consent to record the user consent for the cookies in the category "Functional". The cookie is used to store the user consent for the cookies in the category "Analytics". ![]() These cookies ensure basic functionalities and security features of the website, anonymously. Necessary cookies are absolutely essential for the website to function properly. The multiple input gates are no different to the simple 2-input gates above, So a 4-input AND gate would still require ALL 4-inputs to be present to produce the required output at Q and its larger truth table would reflect that. Logic FunctionĢ-input logic gate truth tables are given here as examples of the operation of each logic function, but there are many more logic gates with 3, 4 even 8 individual inputs. The following Boolean Algebra truth tables gives a list of the common logic functions and their equivalent Boolean notation. The following Boolean ALgebra Truth Tables compare the logical functions of the 2-input logic gates above. Symbolįor a 2-input Ex-NOR gate, the output Q is true if BOTH input A and input B are the same, either true or false, giving the Boolean Expression of: ( Q = (A and B) or (NOT A and NOT B) ). However, as they are widely used functions they are now available in standard IC form and have been included here as reference.įor a 2-input Ex-OR gate, the output Q is true if EITHER input A or if input B is true, but NOT both giving the Boolean Expression of: ( Q = (A and NOT B) or (NOT A and B) ). The switching actions of both of these types of gates can be created using the above standard logic gates. The Boolean expression to indicate an Exclusive-OR or Exclusive-NOR function is to a symbol with a plus sign inside a circle, ( ⊕ ). SymbolĪs well as the standard logic gates there are also two special types of logic gate function called an Exclusive-OR Gate and an Exclusive-NOR Gate. Symbolįor a 2-input NOR gate, the output Q is true if BOTH input A and input B are NOT true, giving the Boolean Expression of: ( Q = not(A OR B) ). 2-input NAND (Not AND) Gateįor a 2-input NAND gate, the output Q is NOT true if BOTH input A and input B are true, giving the Boolean Expression of: ( Q = not(A AND B) ). The NAND and the NOR Gates are a combination of the AND and OR Gates respectively with that of a NOT Gate (inverter). Symbolīoolean Algebra Truth Tables For The NOT Gateįor a single input NOT (Inverter) gate, the output Q is ONLY true when the input is “ NOT” true, the output is the inverse or complement of the input giving the Boolean Expression of: ( Q = NOT A ). Boolean Algebra Truth Tables For A 2-input OR Gateįor a 2-input OR (Inclusive-OR) gate, the output Q is true if EITHER input A “ OR” input B is true, giving the Boolean Expression of: ( Q = A or B ). Note that the Boolean Expression for a two input AND gate can be written as: A.B or just simply AB without the decimal point. Then the four possible combinations of A and B for a 2-input logic gate is given as: However, when dealing with Boolean expressions and especially logic gate truth tables, we do not general use “ON” or “OFF” but instead give them bit values which represent a logic level “1” or a logic level “0” respectively. There are “four” possible input combinations or 2 2 of “OFF” and “ON” for the two inputs. A logic gate truth table shows each possible input combination to the gate or circuit with the resultant output depending upon the combination of these input(s).įor example, consider a single 2-input logic circuit with input variables labelled as A and B. The table used to represent the boolean expression of a logic gate function is commonly called a Truth Table. As well as a standard Boolean Expression, the input and output information of any Logic Gate or circuit can be plotted into standard Boolean Algebra truth tables to give a visual representation of the switching function of the system.
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