# Introduction. Logic. Most Difficult Reading Topics. Basic Logic Gates Truth Tables Logical Functions. COMP370 Introduction to Computer Architecture

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1 Introduction LOGIC GATES COMP370 Introduction to Computer Architecture Basic Logic Gates Truth Tables Logical Functions Truth Tables Logical Expression Graphical l Form Most Difficult Reading Topics Logic gates and figuring out how to read them Logical Circuit Equivalence NAND NOR and XOR truth tables Using the rules to create and read the logic gates using 0's and 1's Transistor implementation Difference between positive logic and negative logic Logic Formal logic is a branch of mathematics ti that t deals with true and false values instead of numbers. In the mid-19 th century, George Bool developed many Logic ideas. Boolean logic deals with equations where the operators are AND or OR instead of add and multiply. 1

2 Electric Logic Logical values can easily be expressed by an electrical l circuit. it True or 1 can be defined as voltage on a wire while False or 0 can be defined as no voltage. We will use positive logic. Analog values can be anything while digital only has discrete values, 0 or 1 Electrical devices called gates can implement the logical Logic Gates & Symbols Note that gates can have more than 2 inputs. AND gate The AND gate is an electronic circuit that gives a true output (1) only if all its inputs are true. A dot ( ) is used to show the AND operation i.e. A B. Note that the dot is sometimes omitted i.e. AB Inputs and Outputs The inputs can be considered as logical (true or false) values. You can also think of the inputs as voltage (true) or ground (false). The output of the gate will also be voltage (true) or ground (false). inputs output 2

3 OR gate The OR gate is an electronic circuit that gives a true output (1) if one or more of its inputs are true. A plus (+) is used to show the OR operation. NOT gate The NOT gate is an electronic circuit that produces an inverted version of the input at its output. It is also known as an inverter. If the input variable is A, the inverted output is known as NOT A. This is also shown as A', or Ā with a bar over the top A A NAND gate NAND gate Cont. This is a NOT-AND gate which is equal to an AND gate followed by a NOT gate. The outputs of all NAND gates are true if any of the inputs are false. The symbol is an AND gate with a small circle on the output. The small circle represents inversion. 3

4 Logical Equivalence A NAND gate gives the same results as an AND gate feeding into a NOT gate. Circuits are logically equivalent if they produce the same truth table output. A B AB NOT AB NAND AB NAND as a NOT Below are two ways that a NAND gate can be configured to produce a NOT gate. They are logically equivalent. It can also be done using NOR logic gates in the same way. A A NAND AA A 1 NAND A NOR gate NOR gate cont. This is a NOT-OR gate which is equal to an OR gate followed by a NOT gate. The outputs of all NOR gates are false if any of the inputs are true. The symbol is an OR gate with a small circle on the output. The small circle represents inversion. 4

5 EXOR gate The 'Exclusive-OR' gate is a circuit which will give a true output t if either, but not both, of its two inputs are true. An encircled plus sign ( ) is used to show the EOR operation. EXNOR gate The'Exclusive-NOR' gate circuit does the opposite to the EOR gate. It will give a false output if either, but not both, of its two inputs are true. The symbol is an EXOR gate with a small circle on the output. The small circle represents inversion. EXNOR gate cont. Logic gate symbols 5

6 Truth Table Logic gates representation using the Truth table Try it Draw the circuit diagrams like the ones below to show how a NOR gate can be made into a NOT gate. NOR Inverter Wiring the NOR gate to become an inverter Three Input AND Gate Here is an example of a three input AND gate. Notice that the truth table for the three input gate is similar to the truth table for the two input gate. It works on the same principle, this time all three inputs need to be true (1) to get a true output. 6

7 Three Input AND Gate Cont. Four Input AND Gate Here is an example of a four input AND gate. It also works on the same principle, all four inputs need to be true (1) to get a true output. The same principles apply to 5, 6,..., n input gates. Four Input AND Gate cont. Two, Three, and Four OR gates 7

8 Connecting Gates The output of one logic gate can be used as the input to another logic gate. The output of one gate can be used as the inputs to several other gates. 8

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