LOGIC GATES
In a digital circuit, logic gates are very important as they define the sequence of procedure in a logical manner under the conditions present in a digital circuit. The input or more are processed to yield a single outcome in a sequence. The digital circuits work at a definite level of voltage. This is because there are binary conditions, 0 or 1, high or low, in any given process in a sequence.
As of the year 2008, there are seven logic gates. Each of them provides a distinct output for any given combination of input. The logic circuits may be cascaded or interconnected to achieve the desired result.
The History and Development of Logic Gates
Nikola Tesla filed for patents of devices containing logic gate circuits in the year 1898. In the subsequent years, the vacuum tubes superseded the relays for processes that require logic gates. In the year 1907, the Fleming valve was modified by Lee De Forest and the outcome of said modification can be used as AND logic gate. Ludwig Wittgenstein published in 1921 a truth table of sixteen rows in his Tractatus Logico-Philosophicus as proposition 5.101. Claude E. Shannon then introduced the Boolean algebra in 1937 as a tool in the analysis and design of switching circuits. The Nobel Prize in physics for the first modern electronic AND gate was awarded to Walther Bothe in 1954 for the invention of the coincidence circuit. Today, molecular logic gates are being developed and explored.
Different Types of Logic Gates
Illustrated below is the Truth Table on how the AND logic gate works. In the AND logic, there must at least be two inputs. In order to yield an output of 1 (true), all the inputs must be 1 (true). If any of the inputs or all of the inputs are 0 (false), the output would also be 0 (false). The operation is like that of multiplication wherein if any of the factor (input) is 0, the product (output) would also be 0. The symbol for the AND logic gate is given below.
AND gate
|
Input 1 |
Input 2 |
Output |
|
0 |
0 |
0 |
|
0 |
1 |
0 |
|
1 |
0 |
0 |
|
1 |
1 |
1 |
The OR logic gate works like the logical inclusive “or.” This means that if any or both of the input is 1 (true), the output would also be 1 (true). If both inputs are 0 (false) the output would be 0 (false). The operation can be compared to that of addition of binary numbers where if any of the factors is 1 the result would also be 1. Provided hereinbelow are the truth table and the symbol for the OR gate.
OR gate
|
Input 1 |
Input 2 |
Output |
|
0 |
0 |
0 |
|
0 |
1 |
1 |
|
1 |
0 |
1 |
|
1 |
1 |
1 |
The XOR (exclusive OR) gate functions similarly with the logical “either/or”. This means that the output would be true only if either input is true. If both input are true, the output would be false. To easily remember this, the inputs must be different to get an output of true. The logic gate XOR symbol and its truth table is given below.
XOR gate
|
Input 1 |
Input 2 |
Output |
|
0 |
0 |
0 |
|
0 |
1 |
1 |
|
1 |
0 |
1 |
|
1 |
1 |
0 |
The inverter, sometimes referred to as the NOT gate functions by reversing or inverting the input. If the input is true, the output would be false and vice versa. This logic gate has one input unlike the other logic gates. The symbol for the inverter and its truth table is given below.
Inverter or NOT gate
|
Input |
Output |
|
1 |
0 |
|
0 |
1 |
The NAND gate is like an AND gate with the output inverted. To easily remember the behavior of the NAND gate, think of it as a NOT AND. Theis is because the output of a NAND gate is exactly the opposite or the inverted output of an AND gate. In NAND gate, the output would be false only and only if both or all inputs are true. The symbol for the NAND gate and its truth table is given below.
NAND gate
|
Input 1 |
Input 2 |
Output |
|
0 |
0 |
1 |
|
0 |
1 |
1 |
|
1 |
0 |
1 |
|
1 |
1 |
0 |
The NOR gate is like an OR gate which output is negated or inverted. Think of it as a NOT OR gate. The output of the NOR gate is the exact opposite of the OR gate. The only condition to get an output of true (1) in NOR gate is when both inputs are false (0). The symbol and the truth table for the NOR gate is given below.
NOR gate
|
Input 1 |
Input 2 |
Output |
|
0 |
0 |
1 |
|
0 |
1 |
0 |
|
1 |
0 |
0 |
|
1 |
1 |
0 |
The XNOR (exclusive NOR) gate is an XOR gate with the output inverted. Think of it as NOT XOR gate. The outputs of the XNOR is the exact opposite of that of an XOR gate. The output is 1 (true) if and only if both inputs are the same. If inputs are different, the output is 0 (false). The symbol and truth table for the XNOR gate is provided below.
XNOR gate
|
Input 1 |
Input 2 |
Output |
|
0 |
0 |
1 |
|
0 |
1 |
0 |
|
1 |
0 |
0 |
|
1 |
1 |
1 |
With all the given discussion of the logic gates, various gates may be combined to suit a particular operation. With the advancement of technology, the logic gates form and function would also become advanced and expand according to the use and function in given tasks.
De Morgan equivalent symbols
De Morgan formulated a theorem of interconnecting logic gates and simplifying it from AND-to-OR equivalent and vice versa. The theorems give way to different rationalization in making circuit diagrams using low signals and in the analysis of the same. The NAND gate can be illustrated as and OR gate with inverted inputs (bubbled inputs). The NOR gate can be shown using AND gate with bubbled inputs. The substitution is convenient in various circuit analysis and give rise to simplification of symbols especially in Boolean operation involving logic gates. De Morgan’s theorem is employed in the transformation of logic gates to NAND or NOR, since in most laboratories keep only NAND and NOR and just convert them whenever other gates are needed for a particular process or operation.