Logical Circuits

Philip Gebhardt3/15/2011

Logic Circuits

•Negative, Positive, and Complimentary circuits• Logic Gates

•Programmable Logic Devices

Logic Circuits are built from Transistors

• Transistors act as the switches in circuits• Controlled by a logical signal from another logic circuit

• The most popular transistor used today• The metal oxide semiconductor field-effect transistor

(MOSFET)• Two different types: n-channel (NMOS) and p-channel

(PMOS)

Negative (NMOS)

Positive (PMOS)

Vx

Vx

X = LOW X = HIGH

X = HIGH X = LOW

NMOS Realization of a NOT gate

Vx

VDD

Vf

X Vf

on off

off on

VDD

Vf = 0

VDD

Vf = VDD

on off

NMOS Realization of the NAND gate

Vy

VDD

Vf

Vx

Vx Vy Vf

0 0 1

0 1 1

1 0 1

1 1 0

NMOS Realization of the AND gate

Vy

VDD

Vx

VDD

Vf

Vx Vy Vf’ Vf

0 0 1 0

0 1 1 0

1 0 1 0

1 1 0 1

Vf ’

NMOS Realization of the AND gate

Vy

VDD

Vx

VDD

Vf

NOT Gate

NAND Gate

NMOS Realization of the NOR gate

Vx Vy

VDD

Vf

NMOS Realization of the OR gate

Vx Vy

VDD VDD

Vf

Complementary MOS (CMOS)

Vy

Vx

Vf

VDDVDD

Vf

Vy

Vx

CMOS NAND gate

CMOS NOR gate

Logic Devices

• 7400 Series Standard Chips• Programmable Logic Devices

• Programmable Logic Array (PLA)• Programmable Array Logic (PAL)• Complex Programmable Logic Devices (CPLDs)

Vy

VDD

Vf

Vx

Logic Devices

• 7400 Series Standard Chips and all other Logic Devices measured in NAND equivalency gates

Logic Devices

• 7400 Series Standard Chips and all other Logic Devices measured in NAND equivalency gates

• Ex: The macrocells in PALs are often about 20 equivalent NAND gates

7400 Series Standard Chips

• External pins used as input/ouput• Two pins used for VDD and GND leads• Multiple chips with different logical gates can

be connected to realize logical functions

F = X1X2 + X2’X3

X1

X2

X3

VDD

F

• Not very efficient for operations with large logical capacity

• Mostly used today as buffers from other logical circuits

Programmable Logic Devices

• PLDs are general-purpose computer chips designed to implement logical circuits.

• Devices with a lot of circuitry and logical gates• Unlike 7400 series chips, has Non-fixed structure

• Can be considered a black box with wide range of logical combinations

• Programmable Logic Array (PLA)• Programmable Array Logic (PAL)

PLD as a Black Box

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Logic GatesAnd SwitchesInput Variables Output Values

(function values)

Programmable Logic Arrays (PLAs)

• PLAs can be broken down into two planes of wires which pass logic gates

• AND plane: logic variables (and their compliments) pass through the AND gates• OR plane: the resultants from the AND gates then pass

through the OR gates

• Switches programmed by the user determine which variable pass through which gates

Generic PLA

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.

.

Input(buffers & inverters)

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AND plane

…

OR planeXn

fm

PLA Implementation

X1, X’1, … Xn, X’n

f1 … fm

Programmable Array Logic

• Unlike PLAs, PALs are not fixed on both logical planes

• Generally only the AND plane fixed

• Less flexibility but more cost efficient and better performance

• Uses extra circuitry after OR gates for more versatility• Macrocells• Flip-flops, MUXs, more buffers

PAL Structure

Programmable switches determine AND gate results…

Fixed OR gates connect to macrocells

Example of macrocell

D Q

CLK

MUX2:1

Back to AND plane

fi

PAL block

Benefits Limitations of PLAs and PALs

• PLAs• Efficient for the area needed for implementation• Too many switches decreases performance and

increases costs for manufacturing

• PALs• Less expensive and easier to manufacture compared to

PLAs• Macrocells allow for implementation of logical circuits

with multiple levels or phases• Less flexibility requires extra circuitry