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# Multiplexing and Demultiplexing - PowerPoint PPT Presentation

Multiplexing and Demultiplexing. In some sense, Multiplexing and Demultiplexing is just a special case of the truth tables we have been studying. You can look under “multiplexor” and “decoder” in the index of Tokheim for more information. . Getting Around.

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Multiplexing and Demultiplexing

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## Multiplexing and Demultiplexing

In some sense, Multiplexing and Demultiplexing is just a special case of the truth tables we have been studying. You can look under “multiplexor” and “decoder” in the index of Tokheim for more information.

### Getting Around

• A fair amount of what goes on inside computers or on computer networks just involves moving data (as opposed to processing that data).

• Most designs have shared information channels (a bus).

• Part of the path used to get from Point A to Point B may also be along the way from Point C to Point D.

• Multiplexing and demultiplexing concerns selecting the data to be transmitted and directing the data to its destination.

### Multiplexing

• Multiplexing is sending more than one signal on a carrier.

• There are two standard types of multiplexing.

• Frequency-Division Multiplexing (FDM): the medium carries a number of signals, which have different frequencies; the signals are carried simultaneously.

• Time-Division Multiplexing (TDM): different signals are transmitted over the same medium but they do so at different times – they take turns.

### Mutiplexing

Multiplexing allows one to select one of the many possible sources.

### Statistical TDM

• In standard TDM, the inputs take turns, one after the other gets to put its information onto the wire.

• In Statistical TDM, the input with the most data or highest priority gets a higher share of the time.

• In this course, our wires hold a single bit of information at a time, so we will focus on a simple type of TDM. It will be somewhat more like statistical TDM in that we will be choosing which input places its information on the wire.

### Multiplexing

• There are several data inputs and one of them is routed to the output (possibly the shared communication channel).

• Like selecting a television channel (although that example is FDM).

• In addition to data inputs, there must be select inputs.

• The select inputs determine which data input gets through.

• How many select pins are needed?

• Depends on number of data inputs.

• All of the (data) inputs at hand are assigned addresses. The address of the data input is used to select which data input is placed on the shared channel.

• So in addition to the collection of data inputs, there are selection (or address) inputs that pick which of the data inputs gets through.

### How many?

• One bit can have two states and thus distinguish between two things.

• Two bits can be in four states and …

• Three bits can be in eight states, …

• N bits can be in 2N states

### Nomenclature

• A Multiplexer is also known as a MUX.

• A MUX has several data inputs and one data output.

• If the MUX has N (possible) data inputs, it is referred to as an N-to-1 MUX.

• Since computers work in binary, the N is usually a power of 2.

• An N-to-1 MUX should have log2(N) address inputs (pins).

### Combinatorial Logic

• A MUX uses combinatorial logic (as opposed to a sequential logic which involves memory).

• The output of a MUX depends solely on the data input and the select input.

• Thus it is just the realization of a truth table.

### Truth table for 2-to-1 MUX

When A=0, Out is same as D0, when A=1, Out is same as D1

### Algebra for 2-to-1 MUX

• Take expressions for 1’s found in truth table

• AD0D1 + AD0D1 + AD0D1 + AD0D1

• This can be factored as follows

• AD0(D1+D1) + A(D0+D0)D1

• (D1+D1) = 1

• Not D1 or D1, doesn’t care about D1

• Note that this factoring/reducing requires the two terms to differ by only one input.

• AD0 + AD1

• (A more general technique for simplifying Boolean expressions uses the Karnaugh map.)

### 4-to-1 MUX: truth table

D0 could be a 1 or a 0, but if A=0 and B=0 then Out is whatever D0 is.

### 4-to-1 MUX: gate version

One output

Many inputs

• Each data input is assigned to a specific state of the select input.

• E.g. low-low, low-high, high-low, high-high

• The state can be interpreted as binary numbers

• 00, 01, 10, 11

• Two select  Four addresses

• And these numbers are thought of as the “addresses” of the input.

### Demultiplexing

• If any of several signals was put onto a single carrier, then at the other end the signals must be separated and each sent to the appropriate destination.

• One input (the shared channel) is routed to one of several outputs.

• Like mail, it is possible for me to send a message to any individual one of you. So there must be a set of paths from me to each of you, and there must be a mechanism for selecting one of those paths in a particular instance.

• In addition to data input, there must be select inputs.

• To select from 2N data outputs requires N select inputs.

### Demultiplexing

Demultiplexing allows one to select one of the many possible destinations.

### Nomenclature

• Demultiplexer a.k.a. DeMUX.

• A DeMUX has one data input and several outputs.

• If the DeMUX has N (possible) data outputs, it may referred to as an 1-to-N DeMUX.

• Since computers work in binary, the N is usually a power of 2.

• An 1-to-N DeMUX should have log2(N) address inputs (pins).

• DeMUX are also sometimes referred to by the number of address pins log2(N)-to-N DeMUX (e.g. 3-to-8 or 2-to-4 DeMUX)

### Combinatorial Logic

• A DeMUX has many outputs.

• Each of those outputs depends only on the input data and the select data (i.e. no memory is involved) .

• Thus a DeMUX is just a realization of a truth table (as is all combinatorial logic).

One input

Many outputs

### Decoder

• A variation on the previous circuit is to have no input data.

• The selected output will be high, the others low.

• Or vice versa.

• This can be used to activate a control pin on the selected part of circuit.

### Decoder plus registers = RAM

• A register is a unit of memory that holds one word of data.

• A typical word may be 32 or 64 bits.

• E.g. the Memory Address Register (MAR) holds an address associated with memory

• Memory (RAM), on the other hand, is a large collection of registers to hold the values of many different words.

• In addition to the registers is a decoder. The decode determines which word one is writing to or reading from.

### Decoder plus registers = RAM

Load pins (allow data into a register)

Only one location selected.

MDR

Decoder

MAR

MAR: Memory Address register holds address one is writing to or reading from

MDR Memory data register holds data being written to or being read from memory.

Addressable set of registers

### ROM is Combinatorial

• In ROM (Read Only Memory), one inputs an address and gets a predetermined output for that address.

• The same input always yields the same output.

• ROM is the realization of a truth table.

• ROM is a way to realize a generic truth table.

• In a way the opposite of what we do with a Karnaugh map. With a K-map we take a specific output and simplify it as much as possible. With ROM, we leave it as generic as possible.

fuse

Decoder

“Burned”

fuse

### Logic of ROM (Cont.)

• Fuses connect output of decoder to output of ROM.

• Normal voltage and current does not burn (“blow”) the fuse.

• So when the selected decoder output is high, all ROM output lines to which it is connected are also high.

### Logic of ROM (Cont.)

• Higher voltage and current will break the connections (a.k.a. burning).

• They are applied selectively to break certain connections.

• The ROM output is not affected by the decoder output if the connection is broken.

• (Implementation may be different, but this is the basic logic).