1 How gates work NOT ( ) NAND ( ) o - - PDF document

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CS240 Computer Organization

Department of Computer Science Wellesley College

Bits and Gates

The digital logic level

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The digital logic level

Conventional Machine Level Micro Programming Level Digitial Logic Level Electronic Circuits Technology of Implementation Computer Science

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Electrical Engineering Solid State Physics Subbasement Basement Ground Floor Level 1 Level 2

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Digital circuits

• A digital circuit is a circuit in which only two logical values

are present.

*Exact voltage levels and their interpretation varies with technology. Low (logic 0; false; unasserted) High (logic 1; true; asserted) Undefined 5 v 2 v 1 v

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Gates

• Tiny electronic devices called gates compute various

functions on these two-valued signals.

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How gates work

• Transistors can be made to behave like very fast binary

switches.

Base Collector +Vcc (Supply Voltage) Emitter (Circuit Ground)

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NOT ( )

Vin +Vcc Vout

NAND ( )

V1

+Vcc Vout

V2

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Integrated Circuits

• Gates are manufactured in units called integrated circuits.

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Wafer, chip, gate

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Wafer, chip, gate

(a) Expose photoresist (b) Wash away unhardened photoresist (c) Etch away uncovered copper (d) Wash away photoresist Mask Light

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The finished product

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Five basic gates

NOT NAND NOR AND OR

*Gates with more then two inputs are possible. Who am I ?

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Design new gates from old

XOR

• The exclusive or is often

used as a one-bit comparator.

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Boolean Algebra

A B A B 1 A B A + B A A A A

*We think of inputs to wires as variables and gates as simple functions.

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Boolean expressions & circuit equivalence

A B = A B A + B A A A A + B 0 + A = A A A = A

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Name that rule

A B = = A + B B A B + A A B C (AB)C AB A B C A(BC) BC

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Name that rule

A A A 0 A = A A A + A =

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Double bubble, toil and trouble

A A + B B A B = A B A B = A B A + B = A + B

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Take care

A 1 A + 1 = A A + AB B = AB

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A universal gate*

*Are there others?

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Circuit simplification

• Can we find a simpler circuit that performs the same

function.*

• Start with an equivalent Boolean expression

F(A, B, C) =

*All things being equal, smaller circuits are cheaper, faster, cooler, and easier to design.

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Voting machines

• A majority circuit outputs

1 whenever a majority of its inputs equal 1.

• We design a simple

majority circuit for three inputs

• A four input AND gate

recognizes exactly one input code.

• What would a code detector

that recognizes 1001 look like?

• What would a code detector

the recognizes either 1001 or 1111 look like?

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Code detectors

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Could be worse*

*Could it be better?