UNIT  II LOGIC GATES AND GATES CLASSIFICATION


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1 UNIT  II Logic Gates: Gates Classifications: Basic Gates (AND, OR, NOT), Universal Gates (NAND, NOR), Exclusive Gates (XOR, XNOR)(except circuit diagram) Logic Symbols, Logic Operators, Logical expression and truth table of Basic, Universal and Exclusive gates. Conversion of Universal Gates to Basic Gates LOGIC GATES AND GATES CLASSIFICATION Logic gates are the basic building blocks of any digital system. It is an electronic circuit having one or more than one input and only one output. The relationship between the input and the output is based on a certain logic. Based on this, logic gates are named as AND gate, OR gate, NOT gate etc. A large number of electronic circuits (in computers, control units, and so on) are made up of logic gates. These process signals which represent true or false. AND Gate The AND gate implements the AND function. With the gate shown to the left, both inputs must have logic 1 signals applied to them in order for the output to be a logic 1. With either input at logic 0, the output will be held to logic 0 Logic diagram
2 OR GATE The AND gate implements the AND function. With the gate shown to the left, both inputs must have logic 1 signals applied to them in order for the output to be a logic 1. With either input at logic 0, the output will be held to logic 0 A circuit which performs an OR operation is shown in figure. It has n input (n >= 2) and one output. The OR gate returns Logic diagram NOT Gate The NOT Gate, or Inverter The inverter is a little different from AND and OR gates in that it always has exactly one input as well as one output. Whatever logical state is applied to the input, the opposite state will appear at the output. The NOT function is denoted by a horizontal bar over the value to be inverted, as shown in the figure to he left. In some cases a single quote mark (') may also be used for this purpose: 0' = 1 and 1' = 0. NOT gate is also known as Inverter. It has one input A and one output Y.
3 Logic diagram NAND GATE The NAND gate implements the NAND function, which is exactly inverted from the AND function you already examined. With the gate shown to the left, both inputs must have logic 1 signals applied to them in order for the output to be a logic 0. With either input at logic 0, the output will be held to logic 1. The circle at the output of the NAND gate denotes the logical inversion Logic diagram
4 NOR GATE The NOR gate is an OR gate with the output inverted. Where the OR gate allows the output to be true (logic 1) if any one or more of its inputs are true, the NOR gate inverts this and forces the output to logic 0 when any input is true. In symbols, the NOR function is designated with a plus sign (+), with an overbar over the entire expression to indicate the inversion. In logical diagrams, the symbol to the left designates the NOR gate. As expected, this is an OR gate with a circle to designate the inversion. Logic diagram XOR GATE The ExclusiveOR, or XOR Gate The ExclusiveOR, or XOR function is an interesting and useful variation on the basic OR function. Verbally, it can be stated as, "Either A or B, but not both." The XOR gate produces a
5 logic 1 output only if its two inputs are different. If the inputs are the same, the output is a logic 0. The XOR symbol is a variation on the standard OR symbol. It consists of a plus (+) sign with a circle around it. The logic symbol, as shown here, is a variation on the standard OR symbol. THE DIGITAL LOGIC EXCLUSIVEOR GATE Symbol B A Q Boolean Expression Q = A B A OR B but NOT BOTH gives Q The truth table above shows that the output of an ExclusiveOR gate ONLY goes HIGH when both of its two input terminals are at DIFFERENT logic levels with respect to each other. If these two inputs, A and B are both at logic level 1 or both at logic level 0 the output is a 0 making the gate an odd but not the even gate. This ability of the ExclusiveOR gate to compare two logic levels and produce an output value dependent upon the input condition is very useful in computational logic circuits as it gives us the following Boolean expression of: Q = (A B) = A.B + A.B
6 THE DIGITAL LOGIC EXNOR GATE Symbol B A Q input ExNOR Gate Boolean Expression Q = A B Read if A AND B the SAME gives Q The logic function implemented by a 2input ExNOR gate is given as when both A AND B are the SAME will give an output at Q. In general, an ExclusiveNOR gate will give an output value of logic 1 ONLY when there are an EVEN number of 1 s on the inputs to the gate (the inverse of the ExOR gate) except when all its inputs are LOW. Then an ExNOR function with more than two inputs is called an even function or modulo2 sum (Mod2SUM), not an ExNOR. This description can be expanded to apply to any number of individual inputs as shown below for a 3input ExclusiveNOR gate. GATE CONVERSION (UNIVERSAL GATES TO BASIC GATES) This is a continuation of previous post, in this post, we will see the NOR gate as a univarsal gate and create different gates using NOR gate. As we know that NAND and NOR Gates are called Universal Gates since they can cerate any of the Logic Gate Lets see to how to make all other logic gates by using the NOR Gate 1. NOR gate to NOT Gate conversion Refer the following diagram Digital : Image NOR to NOT
7 NOR to NOT Conversion Here the same input is applied to the both inputs of a NOR Gate According to NOR Gate If A and B are two inputs than output equation will be (A+B) For this case : = (X+X) = X = Inverted Input 2. NOR Gate to AND Gate Convertion Refer following diagram for NOR to AND Gate conversion Digital : Image NOR to AND Conversion NOR to AND Conversion According to diagram s1 = (X+X) = X s2 = (Y+Y) = Y s3= (s1+s2) = (X +Y ) => (X ).(Y )
8 => X.Y => AND Gate 3. NOR Gate to OR Gate Convertion Refer the following Diagram Digital : Image NOR to OR Convertion NOR to OR For this case X and Y are the two inputs to a NOR gate and the output of the First NOR gate goes again to an another NOR gate s inputs. => s1 = (X+Y) => s2 = (s1+s1) = s1 => s2 = ((X+Y) ) => X+Y => OR Gate 4. NOR Gate to NAND Gate Convertion Refer the following Diagram Digital : Image NOR to NAND NOR to NAND Conversion
9 According to diagram s1 = (X+X) = X s2 = (Y+Y) = Y s3 = (s1+s2) = (X +Y ) => (X ).(Y ) => X.Y s4 = (s3 + s3) => s3 => (X.Y) => NAND Gate Questions and Answer Hints Explain Basic Gates (Ans Hint : AND, OR, NOT) Explain Universal Gates (Ans : NAND, NOR, XOR, XNOR) What is Logical Operators (Explain the Logical Gates and the output with truth table and expressions) What is Gate Conversion? and Explain with example.(write the answer how to convert basic gates to universal gates_
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