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### Digital logic

• 1. DIGITAL LOGIC  What is gate?  The Basic Gates  NOT gate  OR gate  AND gate  Universal Logic Gates  NOR gate  NAND gate 1 Presented by, M.Madhu Bala
• 2. GATES  A digital circuit having one or more input signals but only one output signal is called a gate.  Connecting the basic gates in different ways makes it possible to produce circuits.  Gates are often called logic circuits.  The basic gates can be used to produce any digital system.  The three basic logic circuits are  the inverter (NOT)  the OR gate and  the AND gate 2
• 3. THE INVERTER (NOT GATE)  A NOT gate has one input signal and one output signal.  The output Y of NOT gate is always complement of input A.  In equation form Y= NOT A Y=A‘ Y=A  There are only two possible voltage levels (low and high) associated with a digital circuit. This fits with the binary number system (0&1)  This is often referred to as two-state operation.  In the positive logic,  the higher voltage level is assigned the binary value 1 (H=1)  the lower voltage level is assigned the binary value 0 .(L=0) 3 A Y=A’ L H H L A Y=A’ 0 1 1 0 Logic Circuit of NOT gate Truth Table
• 4. THE INVERTER (NOT GATE) TTL NOT Gates Pinout diagram of a 7404 hex inverter  This IC contains six inverters.  After applying +5 V to pin 14 and grounding pin 7, you can connect any or all inverters to other Transistor–Transistor Logic(TTL) devices. 4
• 5. OR GATE  An OR gate has two or more input signals but only one output signal.  It is called an OR gate because the output voltage is high if any or all of the input voltages are high.  In Boolean equation form Y = A OR B Y = A + B The '+' sign represents the logic operation OR  The number of rows in a truth table equals 2n, where n is the number of inputs 5 Logic Circuit of OR gate A B Y=A+B 0 0 0 0 1 1 1 0 1 1 1 1 Truth Table
• 6. Three- input OR gate  The inputs are A, B, and C.  When all inputs are low, the output is low.  If any input is high, the output will be high.  Boolean Equation Form: Y = A+B+C 6 OR GATE (CONT..) A B C Y=A+B+C 0 0 0 0 0 0 1 1 0 1 0 1 0 1 1 1 1 0 0 1 1 0 1 1 1 1 0 1 1 1 1 1Logic Circuit of 3-input OR gate Truth Table
• 7. TTL OR Gates This digital IC contains four 2-input OR gates inside a 14- pin DIP. After connecting a supply voltage of +5 V to pin 14 and a ground to pin 7, you can connect one or more of the OR gates to other TTL devices. 7 OR GATE (CONT.)
• 8. Timing diagram for 2-input OR gate  The input voltages drive pins 1 and 2 of a 7432.  The output (pin 3) is low only when both inputs are low.  The output is high the rest of the time. 8 OR GATE (CONT..)
• 9.  The AND gate has a high output only when all inputs are high. otherwise the output will be low.  AND gate also known as all-or-nothing gate.  In Boolean equation form Y =A AND B Y=A.B Y=AB The '.' sign represents the logic AND operation. 9 AND GATE A B Y=AB 0 0 0 0 1 0 1 0 0 1 1 1Logic Circuit of AND gate Truth Table
• 10. Three- input AND gate  The inputs are A, B, and C.  When all inputs are high, the output is high.  If even one input is low, the output is in the low state.  In Boolean equation form: Y=A.B.C Y=ABC 10 AND GATE (CONT..) A B C Y=ABC 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 0 1 0 0 0 1 0 1 0 1 1 0 0 1 1 1 1 Logic Circuit of AND gate Truth Table
• 11. TTL AND Gates  This digital IC contains four 2-input AND gates.  After connecting a supply voltage of +5V to pin 14 and a ground to pin 7, you can connect one or more of the AND gates to other TTL devices.  TTL AND gates are also available in triple 3-input and dual 4-input packages. 11 AND GATE (CONT..)
• 12. Timing diagram for a 2-input AND gate The input voltages drive pins 1 and 2 of a 7408. the output (pin 3) is high only when both inputs are high. The output is low the rest of the time. 12 AND GATE (CONT..)
• 13. The NAND & NOR gates are called universal gates because they can perform all the logical operations of basis gates like AND, OR, NOT. 13 Universal Logic Gate
• 14.  The circuit of NOR gate is a circuit of OR gate followed by an inverter  The output of NOR gate is Y=A+B  NOR Gates also called a NOT-OR gate.  All inputs must be low to get a high output.  If any input is high, the output is low. 14 NOR GATE Logic Circuit of NOR Gates Abbreviated form Standard form IEEE form Truth Table A B Y=(A+B)’ 0 0 1 0 1 0 1 0 0 1 1 0
• 15. Pin- out Diagram of NOR gate 15 NOR GATE (CONT.)
• 16. Bubbled AND Gate  Bubbled AND Gate inverters on the input lines of an AND gate.  The output of bubbled AND gate and NOR gate are identical.  Therefore, these two circuits are equivalent and thus interchangeable.  The output of bubbled AND gate is represented as Y= A . B 16 NOR GATE (CONT.) Abbreviated form Standard form Truth Table A B A’ B’ Y=A’.B’ 0 0 1 1 1 0 1 1 0 0 1 0 0 1 0 1 1 0 0 0 Logic Circuit of Bubbled AND Gates
• 17. De Morgan's First Theorem NOR gate : Y=(A+B)’ bubbled AND gate : Y=A’B’  The outputs are equal for the same inputs, so that (A+B)’ = A’B’  The complement of a sum equals the product of the complements. This identity is known as De Morgan’s, first theorem.  This can also be proved by comparing the truth tables of NOR and bubbled AND gates.  Three input NOR gate and three input bubbled AND gate are identical and it can write, (A+ B + C)' = A'B'C'  This equivalence can be extended to gates or circuits for larger number of inputs, too. 17 NOR GATE (CONT.)
• 18. NOT from NOR  To get a NOT gate, tie inputs of NOR gate together so that there is only one input to the circuit.  If input is 0, then both the inputs to NOR gate are 0 that gives output 1.  Similarly, if input is 1, both the inputs to NOR gate are 1 that gives output 0.  Therefore the output of circuit is complement of its input and thus gives NOT operation. 18 NOR GATE (CONT.)
• 19. OR from NOR  To get a OR gate, two NOR gates are used.  The first NOR gate performs usual NOR operation.  The second NOR gate performs as NOT gate and inverts the NOR logic to OR 19 NOR GATE (CONT.) A+B
• 20. AND from NOR  To get a AND gate, three NOR gates are used.  The first and second NOR gate performs as NOT gate.  NOT gates are replaced by NOR equivalent. Since NOR gate is NOT operation followed by OR we invert the  output of example 2.3, shown in Fig. 2.9b to get output of this circuit. Thus output of circuit in Fig. 2.2 lc is  high only when both the inputs are high and it functions like an AND gate. 20 NOR GATE (CONT.)
• 21.  The circuit of NAND gate is a circuit of AND gate followed by an inverter  The output of NAND gate is Y=AB "Y equals NOT A AND B"  NAND Gates also called a NOT-AND gate.  All inputs must be high to get a low output.  If any input is low, the output is high. 21 NAND GATE Logic Circuit of NAND Gate Abbreviated form Standard form IEEE form Truth Table A B AB Y=AB 0 0 0 1 0 1 0 1 1 0 0 1 1 1 1 0
• 22. Pin- out Diagram of NAND gate 22 NAND GATE (CONT.)
• 23. Bubbled OR Gate  Bubbled OR Gate inverters on the input lines of an OR gate.  The output of bubbled OR gate and NAND gate are identical.  Therefore, these two circuits are equivalent and thus interchangeable.  The output of bubbled OR gate is represented as Y=A+B 23 NAND GATE (CONT.) A B A B Y=A+B 0 0 1 1 1 0 1 1 0 1 1 0 0 1 1 1 1 0 0 0 Abbreviated form Standard form Truth TableLogic Circuit of Bubbled OR Gate
• 24. De Morgan's Second Theorem NAND Gate :(AB)’ Bubbled OR Gate : Y=A’+B’  The outputs are equal for the same inputs, so that (AB)’ = A’+B’  The complement of a product equals the sum of the complements. This identity is known as De Morgan’s second theorem.  This can also be proved by comparing the truth tables of NAND gate and bubbled OR gate.  Three input NAND gate and three input bubbled OR gate are identical and it can write, (ABC)' = A’+B‘+C’  This equivalence can be extended to gates or circuits with any number of inputs. 24 NAND GATE (CONT.)
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