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

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MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 2 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

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MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 3 Logic Gates

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

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

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

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

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

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

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

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MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 11 Draw Logic Gates When Boolean expression is obtained, we can draw logic gates Example: –F1 = xyz (use three input AND gate)

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

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MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 13 Logic Circuit Analysis When logic circuit is given, we can analyze the circuit to obtain logical expression Example: –What is the Boolean expression for F4

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MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 14 Logic Circuit Analysis What is the Boolean expression for F5

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MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 15 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 transistors number –Self sufficient (can build any gate from it) NAND/NOR: save, self sufficient XOR: useful (e.g. execute parity bit)

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MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 16 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

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

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

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

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MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 20 Build using NAND gate It is not impossible to build Boolean expression using NAND gates Steps –Obtain sum-of-product Boolean expression E.g: F3 = xy +xz –Use DeMorgan theorem to get expression using two level NAND gate E.g: F3 = xy +xz = (xy+xz) = ((xy).(xz))

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

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MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 22 Build using NOR gate It is not impossible to build Boolean expression using NOR gates Steps –Obtain product-of-sum Boolean expression E.g: F6 = (x+y).(x+z) –Use DeMorgan theorem to get expression using two level NAND gate E.g: F3 = (x+y).(x+z) =((x+y).(x+z)) = ((x+y)+(x+z))

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

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

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MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 25 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

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

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MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 27 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

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

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MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 29 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

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

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