Introduction to Logic Gates Logical gates Inverter AND

  • Slides: 30
Download presentation
Introduction to Logic Gates • Logical gates – – – – Inverter AND OR

Introduction to Logic Gates • Logical gates – – – – Inverter AND OR NAND NOR Exclusive OR (XOR) Exclusive NOR (XNOR) • Draw Logic Circuit • Analysis of Logic Circuit MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 1

Introduction to Logic Gates • Universal gates NAND and NOR – NAND gate –

Introduction to Logic Gates • Universal gates NAND and NOR – NAND gate – NOR gate • • • Execution using NAND gate Execution using NOR gate Positive & Negative Logic SOP Expression Execution POS Expression Execution Integrated Logic Circuit Family MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 2

Logic Gates MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 3

Logic Gates MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 3

Logic Gates • Inverter gate • The use of inverter: complement MOHD. YAMANI IDRIS/

Logic Gates • Inverter gate • The use of inverter: complement MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 4

Logic Gates • AND gate MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 5

Logic Gates • AND gate MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 5

Logic Gates • OR gate MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 6

Logic Gates • OR gate MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 6

Logic Gates • NAND gate MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 7

Logic Gates • NAND gate MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 7

Logic Gates • NOR gate MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 8

Logic Gates • NOR gate MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 8

Logic Gates • Exclusive OR (XOR) gate MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 9

Logic Gates • Exclusive OR (XOR) gate MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 9

Logic Gates • Exclusive NOR (XNOR) gate MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 10

Logic Gates • Exclusive NOR (XNOR) gate MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 10

Draw Logic Gates • When Boolean expression is obtained, we can draw logic gates

Draw Logic Gates • When Boolean expression is obtained, we can draw logic gates • Example: – F 1 = xyz’ (use three input AND gate) MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 11

Draw Logic Gates MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 12

Draw Logic Gates MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 12

Logic Circuit Analysis • When logic circuit is given, we can analyze the circuit

Logic Circuit Analysis • When logic circuit is given, we can analyze the circuit to obtain logical expression • Example: – What is the Boolean expression for F 4 MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 13

Logic Circuit Analysis • What is the Boolean expression for F 5 MOHD. YAMANI

Logic Circuit Analysis • What is the Boolean expression for F 5 MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 14

Universal Gates: NAND & NOR • Gate AND/OR/NOT is enough to build any Boolean

Universal Gates: NAND & NOR • Gate AND/OR/NOT is enough to build any Boolean function • Even though, other gates is also used because: – Very useful (no choice) – Save transistor’s number – Self sufficient (can build any gate from it) NAND/NOR: save, self sufficient XOR: useful (e. g. execute parity bit) MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 15

NAND Gate • NAND gate is self sufficient (i. e. can build any gate

NAND Gate • NAND gate is self sufficient (i. e. can build any gate from it) • Can be used for building AND/OR/NOT gate • Build NOT gate using NAND gate MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 16

NAND Gate • Build AND gate using NAND gates • Build OR gate using

NAND Gate • Build AND gate using NAND gates • Build OR gate using NAND gates MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 17

NOR Gate • NOR gate is also self sufficient • Can be used for

NOR Gate • NOR gate is also self sufficient • Can be used for building AND/OR/NOT gate • Build NOT gate using NOR gate MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 18

NOR Gate • Build AND gate using NOR gates • Build OR gate using

NOR Gate • Build AND gate using NOR gates • Build OR gate using NOR gates MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 19

Build using NAND gate • It is not impossible to build Boolean expression using

Build using NAND gate • It is not impossible to build Boolean expression using NAND gates Steps – Obtain sum-of-product Boolean expression • E. g: F 3 = xy’ +x’z – Use De. Morgan theorem to get expression using two level NAND gate • E. g: F 3 = xy’ +x’z = (xy’+x’z)” = ((xy’)’. (x’z)’)’ MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 20

Build using NAND gate MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 21

Build using NAND gate MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 21

Build using NOR gate • It is not impossible to build Boolean expression using

Build using NOR gate • It is not impossible to build Boolean expression using NOR gates Steps – Obtain product-of-sum Boolean expression • E. g: F 6 = (x+y’). (x’+z) – Use De. Morgan theorem to get expression using two level NAND gate • E. g: F 3 = (x+y’). (x’+z) =((x+y’). (x’+z))’’ = ((x+y’)+(x’+z)’)’ MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 22

Build using NOR gate MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 23

Build using NOR gate MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 23

Positive & Negative Logic • In logic gate, most of the time – H

Positive & Negative Logic • In logic gate, most of the time – H (High Voltage, 5 V) = logic 1 – L (Low Voltage, 0 V) = logic 0 • This is called positive logic • However, if it is inverted, it is negative logic – H (High Voltage, 5 V) = logic 0 – L (Low Voltage, 0 V) = logic 1 • Depends, some similar gate need different Boolean function MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 24

Positive & Negative Logic • Signal which is set to logic 1 is said

Positive & Negative Logic • Signal which is set to logic 1 is said to be active and true • Signal which is set to logic 0 is said to be not active and false • The name of active high signal is always written in non-compliment form • The name of active low signal is always written in non-compliment form MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 25

Positive & Negative Logic MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 26

Positive & Negative Logic MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 26

Construction of SOP Expression • Sum-of-product expression can be built using – Two level

Construction of SOP Expression • Sum-of-product expression can be built using – Two level logic gate AND-OR – Two level logic gate AND-NOT • Logic AND-OR gate MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 27

Construction of SOP Expression • NAND-NAND circuit (with transformation circuit) – Add two balls

Construction of SOP Expression • NAND-NAND circuit (with transformation circuit) – Add two balls – Change OR with NAND with inverted input and ball on it’s compliment input MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 28

Construction of POS Expression • Product-of-sum expression can be built using – Two level

Construction of POS Expression • Product-of-sum expression can be built using – Two level logic gate AND-OR – Two level logic gate AND-NOT • Logic AND-OR gate MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 29

Construction of POS Expression • NOR-NOR circuit (with transformation circuit) ”: – Add two

Construction of POS Expression • NOR-NOR circuit (with transformation circuit) ”: – Add two balls – Change AND with NOR with inverted input and ball on it’s compliment input MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 30