skip instructionseTEACH presentation accessible player instructions

This eTEACH player requires that you have Flash 8 or above installed. If you do not, download the player from Adobe.

The next major heading marks the start of the presentation. Each next lower level heading thereafter marks the beginning of a slide. An audio control button that plays the audio track for the slide follows the contents and notes for each slide in the presentation. Pressing this button after the audio playback toggles pausing and resuming the playback. Before moving off the play audio button, complete listening to the audio track for the slide or pause the audio. Control + Shift + L increases volume. Control + Shift + Q decreases volume.

There is a table of contents for the presentation following the presentation. The table of contents can be used to access sections of the presentation in random order. Type Control + Shift + C to go to the table of contents.

When links to external resources are present in the presentation, a list of these resource links follows the table of contents. When following a link to a resource, you should remember which slide you were on. When you return to the main page, your screen-reader may not return you to that slide. You can use the table of contents or just click through the headings to return to the correct slide.

This presentation contains resources. Click here to proceed immediately to the resource list. A link to resources follows each slide.

If the presentation contains one or more quizzes, a button to take you to each quiz follows the slide at which the quiz is to occur. Each question in the quiz begins with a level three heading. The answer choices will be presented in a list. If your instructor has supplied a hint for the questions, it will follow the answers and is formatted as an anchor. The correct answer to the question follows the list of answers and the hint (if included). The correct answer is also formatted as an anchor.

Chapter 2 - Part 1 - PPT - Mano & Kime - 2nd Ed

Slide 1 Lecture 14 Combinational Functional Blocks

Lecture 14 Combinational Functional Blocks

Slide 2 Overview

Overview Functions and functional blocks Enabling Decoding Encoding Selecting

Slide 3 Functions and Functional Blocks

Functions and Functional Blocks Higher-level functions Common in real designs Simplify design process Add hierarchy and replication Implemented within a functional block. In the past, many functional blocks were implemented as SSI, MSI, and LSI chips. Today, they are often simply parts within a VLSI circuits.

Slide 4 Enabling Function

Enabling Function Enabling permits an input signal to pass through to an output Disabling blocks an input signal from passing through to an output, replacing it with a fixed value The value on the output when it is disable can be Hi-Z (as for three-state buffers and transmission gates), 0 , or 1 When disabled, 0 output When disabled, 1 output See Example 4-2 in text Adobe Systems

Slide 5 Decoding

Decoding - the Conversion of n-bit input to m-bit output Given n £ m £ 2n Circuits that perform decoding are called decoders Called n-to-m line decoders, where m £ 2n, and Generate 2n (or fewer) minterms for the n input variables Decoding

Slide 6 Decoder Examples

1-to-2-Line Decoder 2-to-4-Line Decoder Note that the 2-4-line made up of 2 1-to-2- line decoders and 4 AND gates. Decoder Examples Adobe Systems Adobe Systems

Slide 7 Decoder Expansion - Example

Decoder Expansion - Example Result Adobe Systems

Slide 8 Decoder with Enable

In general, attach m-enabling circuits to the outputs See truth table below for function Note use of X s to denote both 0 and 1 Combination containing two X s represent four binary combinations Alternatively, can be viewed as distributing value of signal EN to 1 of 4 outputs In this case, called a demultiplexer Adobe Systems Decoder with Enable

Slide 9 Encoding

Encoding Encoding - the opposite of decoding Conversion of m-bit input to n-bit output Circuits that perform encoding are called encoders An encoder has 2n (or fewer) input lines and n output lines which generate the binary code corresponding to the input values Typically, an encoder converts a code containing exactly one bit that is 1 to a binary code corres-ponding to the position in which the 1 appears.

Slide 10 Encoder Example

Encoder Example A decimal-to-BCD encoder Inputs: 10 bits corresponding to decimal digits 0 through 9, (D0, …, D9) Outputs: 4 bits with BCD codes Function: If input bit Di is a 1, then the output (A3, A2, A1, A0) is the BCD code for i, The truth table could be formed, but alternatively, the equations for each of the four outputs can be obtained directly.

Slide 11 Encoder Example (continued)

Encoder Example (continued) Input Di is a term in equation Aj if bit Aj is 1 in the binary value for i. Equations: A3 = D8 + D9 A2 = D4 + D5 + D6 + D7 A1 = D2 + D3 + D6 + D7 A0 = D1 + D3 + D5 + D7 + D9

Slide notes

No. The total gate input cost remains the same.

Slide 12 Priority Encoder

Priority Encoder What if multiple inputs are true? Encoder just designed does not work. Instead, use a priority encoder. Encodes either Most significant input position Or least significant input position

Slide 13 Priority Encoder Example

Priority Encoder Example Priority encoder with 5 inputs (D4, D3, D2, D1, D0) - highest priority to most significant 1 present - Code outputs A2, A1, A0 and V where V indicates at least one 1 present. Xs in input part of table represent 0 or 1; thus table entries correspond to product terms instead of minterms. The column on the left shows that all 32 minterms are present in the product terms in the table

Slide notes

Go over table explaining how entries were obtained, particularly those containing Xs

Slide 14 Priority Encoder Example (continued)

Priority Encoder Example (continued) Could use a K-map to get equations, but can be read directly from table and manually optimized if careful: A2 = D4 A1 = D3 + D2 = F1, F1 = (D3 + D2) A0 = D3 + D1 = (D3 + D1) V = D4 + F1 + D1 + D0 D4 D3 D4 D4 D4 D3 D4 D2 D4 D2

Slide 15 Selecting

Selecting of data or information is a critical function in digital systems and computers Circuits that perform selecting have: A set of information inputs from which the selection is made A single output A set of control lines for making the selection Logic circuits that perform selecting are called multiplexers Selecting can also be done by three-state logic or transmission gates Selecting

Slide 16 Multiplexers

Multiplexers A multiplexer selects one input line and transfers it to output n control inputs (Sn - 1, … S0) called selection inputs m £ 2n information inputs (I2n - 1, … I0) output Y

Slide 17 2-to-1-Line Multiplexer

2-to-1-Line Multiplexer Since 2 = 21, n = 1 The single selection variable S has two values: S = 0 selects input I0 S = 1 selects input I1 The equation: Y = I0 + SI1 The circuit: S Adobe Systems

Slide 18 2-to-1-Line Multiplexer (continued)

2-to-1-Line Multiplexer (continued) Note the regions of the multiplexer circuit shown: 1-to-2-line Decoder 2 Enabling circuits 2-input OR gate To obtain a basis for multiplexer expansion, we combine the Enabling circuits and OR gate into a 2 ´ 2 AND-OR circuit: 1-to-2-line decoder 2 ´ 2 AND-OR In general, for an 2n-to-1-line multiplexer: n-to-2n-line decoder 2n ´ 2 AND-OR Adobe Systems

Slide 19 Example: 4-to-1-line Multiplexer

Example: 4-to-1-line Multiplexer 2-to-22-line decoder 22 ´ 2 AND-OR Adobe Systems

Slide 20 Multiplexer Width Expansion

Multiplexer Width Expansion Select vectors of bits instead of bits Use multiple copies of 2n ´ 2 AND-OR in parallel Example: 4-to-1-line quad multi- plexer Adobe Systems

Slide 21 Other Selection Implementations

Other Selection Implementations Three-state logic in place of AND-OR Gate input cost = 14 compared to 22 (or 18) for gate implementation Adobe Systems

Slide 22 Other Selection Implementations

Other Selection Implementations Transmission Gate Multiplexer Gate input cost = 8 compared to 14 for 3-state logic and 18 or 22 for gate logic Adobe Systems

Slide 23 Summary

Summary Functions and functional blocks Enabling Decoding Encoding Selecting with multiplexers

End of slides

Table of Contents

The object immediately following this sentence is the media player.

You need to upgrade your Flash Player.
Please download and install the latest Flash Player.
If you have the latest Flash Player and are still seeing this message, proceed.