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Computer Science 210 Computer Organization Introduction to Logic Circuits

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From Boolean Logic to Hardware Boolean values true and false map to binary values 1 and 0 Binary values 1 and 0 map to discrete states on and off Discrete states on and off map to voltage levels +5V and 0V on an analog device Connect these devices to perform logical operations

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Transistor - Electronic Switch Collector Base EmitterSwitch Base High (+5v or 1) Makes connection Base Low (0v or 0) Disconnects

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AND Gate +5v Output is 1 only if –Input-1 is 1 and –Input-2 is 1 Output = Input1 AND Input2 Output Input-1Input-2 AND Gate A ABB

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OR Gate Output is 1 if –A is 1 or if –B is 1 Output = A OR B +5v Output A B OR Gate A A + B B

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NOT Gate +5v Input Ground Input High (+5v or 1) Output Low (0v or 0) Input Low (0v or 0) Output High (+5v or 1) Output is opposite of Input Output NOT Gate A _A_A

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Basic Gates AND Gate A ABB OR Gate A A + B B NOT Gate A _A_A NAND Gate A B ___ AB NOR Gate A B _____ A + B

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Boolean Exp Logic Circuit To draw a circuit from a Boolean expression: – From the left, make an input line for each variable. – Next, put a NOT gate in for each variable that appears negated in the expression. – Still working from left to right, build up circuits for the subexpressions, from simple to complex.

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Logic Circuit: _ ____ AB+(A+B)B A B Input Lines for Variables

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Logic Circuit: _ ____ AB+(A+B)B A B NOT Gate for B _B_B

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Logic Circuit: _ ____ AB+(A+B)B A B _ Subexpression AB _B_B _ AB

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Logic Circuit: _ ____ AB+(A+B)B A B Subexpression A+B _B_B _ AB A+B

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Logic Circuit: _ ____ AB+(A+B)B A B ___ Subexpression A+B _B_B _ AB A+B ____ A+B

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Logic Circuit: _ ____ AB+(A+B)B A B ___ Subexpression (A+B)B _B_B _ AB A+B ____ A+B ____ (A+B)B

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Logic Circuit: _ ____ AB+(A+B)B A B Entire Expression _ AB A+B ____ A+B _B_B ____ (A+B)B

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The Boolean Triangle Boolean Expression Truth Table Logic Circuit

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