Documentation Standards

• Circuit specification.– Description of what the system

is supposed to do, including a description of all inputs and outputs and the functions that are to be performed (page 312).

• Block diagram.– Informal pictorial description

of the system’s major functional modules.

• Schematic or logic diagram.– Formal specification of the

electrical components of the system, their interconnections, and all details needed to construct it (IC type, pin numbers, etc.).

Documentation Standards

• Timing diagram.– Shows the values of various

logic signals as a function of time, including cause and effect delays between critical signals.

• Structured logic device description.– Describes the internal function

of a programmable logic device (PLD), a field programmable gate array (FPGA) or an application specific integrated circuit (ASIC).

Block Diagrams

Block Diagrams

Gate Symbols

SSI

Active Levels For Pins• Each signal should have an

active level associated with it.• A signal is active high if it

performs the named action or denotes the named condition when it is HIGH or 1.

• A signal is active low if it performs the named action or denotes the named condition when it is LOW or 0.

• A signal is said to be asserted when it is at its active level.

Active Levels For Pins

Buses• Collection of two or more

related signal lines.

Timing Diagrams• Illustrate the logical behavior

of the signals in a digital circuit as a function of time.

• Causality: which input transition causes which output transition.

• Propagation delay: the time it takes for a change at the input to produce a change at the output.– Note that propagation delays

when outputs change from LOW to HIGH may differ from when they change from HIGH to LOW.

Timing Diagrams

Decoders• A decoder is a multiple-input

multiple-output logic circuit that converts coded inputs into coded outputs, where the inputs and outputs codes are different.

Decoders• Generally the input code has

fewer bits than the output codes.

• In a one-to-one mapping each input code word produces a different output code word.

• Most commonly used codes:– For input:

• The n-bit binary code.– For output:

• The 1-out-of-m code.

Binary Decoder• Binary decoder:

– The most common decoder.– n-to-2n.– The input code is the n-bit

binary code.– The output code is the 1-out-of-

m code.

Binary Decoder

Binary Decoder

Binary Decoder

Cascading Binary Decoders

Cascading Binary Decoders

Seven Segment Decoders

Seven Segment Decoders

Encoders• Reverses what a decoder does.• If a device’s output code word

has fewer bits than the input code word then the device is usually called an encoder.

• The simplest encoder is the binary encoder or the 2n-to-n encoder.

Encoders

I0 I1 I2 I3 I4 I5 I6 I7 Y2 Y1 Y01 0 0 0 0 0 0 0 0 0 00 1 0 0 0 0 0 0 0 0 10 0 1 0 0 0 0 0 0 1 00 0 0 1 0 0 0 0 0 1 10 0 0 0 1 0 0 0 1 0 00 0 0 0 0 1 0 0 1 0 10 0 0 0 0 0 1 0 1 1 00 0 0 0 0 0 0 1 1 1 1

Inputs Outputs

Priority Encoders• Priority encoders assigns

priority to the input lines, so that when multiple lines are asserted at the same time, the encoder will produce the highest priority requestor.

I0 I1 I2 I3 I4 I5 I6 I7 Y2 Y1 Y01 0 0 0 0 0 0 0 0 0 0X 1 0 0 0 0 0 0 0 0 1X X 1 0 0 0 0 0 0 1 0X X X 1 0 0 0 0 0 1 1X X X X 1 0 0 0 1 0 0X X X X X 1 0 0 1 0 1X X X X X X 1 0 1 1 0X X X X X X X 1 1 1 1

Inputs Outputs

Priority Encoders

Cascading Binary Encoders

Tri-State Devices• Devices whose outputs may be

in one of three states, 0, 1, or Hi-Z (high impedance).

• These devices have an extra input which is used to control if the output is floating (Hi-Z) or if it is behaving normally (page 385).

OutputEN A Y0 0 00 1 11 X Hi-Z

Inputs

Tri-State Devices

Tri-State Devices

Tri-State Devices

Tri-State Devices

Multiplexers

• Digital switch (page 398).• A multiplexer with n data

sources requires s = log2 n select lines.

• Commercially available MUX have n= 1, 2, 4, 8 or 16.

• EN enables the output.

Multiplexers

• Y = EN S’ D0 + EN S D1

OutputEN S D0 D1 Y0 X X X 01 0 0 0 01 0 0 1 01 0 1 0 11 0 1 1 11 1 0 0 01 1 0 1 11 1 1 0 01 1 1 1 1

Inputs

OutputEN S Y0 X 01 0 D01 1 D1

Inputs

Multiplexers

• General logic equation for a multiplexer is show above.

1

0

iDMENiYn

jjj

Multiplexers

Multiplexers

Multiplexers

Multiplexers

Demultiplexers

• Digital switch (page 405).• A demultiplexer with n data

outputs requires s = log2 n select lines.

Demultiplexers

Exclusive-Or Gates• An exclusive-or (XOR) gate is

a 2 input device whose output is 1 if exactly one of its inputs is 1 (page 410).

• An exclusive-nor (XNOR) or equivalence is just the opposite.

Exclusive-Or Gates

Parity Circuits• Parity detectors are circuits

that detects if the numbers of ones at its input is odd or even.

• Used to detect errors during the transmission of binary information, by using a parity bit.

• Parity bit is an extra bit included with the binary message to make the number of ones in the message either even or odd.

Parity Circuits

Parity Circuits

Parity Circuits

Comparators

• Comparators are circuits that compare two binary words and indicates whether they are equal or not equal.

Comparators

Comparators

Comparators

Adders

• Half adder adds two one bit operands and produces a two bit sum (page 431).

• HS = X Y• CO = XY

X Y CO HS0 0 0 00 1 0 11 0 0 11 1 1 0

Adders• Full adder adds three one bit

operands and produces a two bit sum.

• S = X Y CIN• COUT = XY + X CIN + Y

CIN

CIN X Y COUT S0 0 0 0 00 0 1 0 10 1 0 0 10 1 1 1 01 0 0 0 11 0 1 1 01 1 0 1 01 1 1 1 1

Adders

PLDs

PLDs

PLDs

PAL16L8

GAL16V8C