Multiplexing and Demultiplexing

Multiplexing There are several data inputs and one of them is routed to the output Like selecting a television channel In addition to data inputs, there must be select inputs How many select pins are needed? Depends on number of inputs Multiplexer aka MUX

Truth table for 2-to-1 MUX Select Data Out S0 A B 1

Algebra for 2-to-1 MUX Take expressions for 1’s found in truth table SAB + SAB + SAB + SAB This can be factored as follows SA(B+B) + S(A+A)B (B+B) = 1 Not B or B, doesn’t care about B SA + SB

Gates for 2-to-1 MUX S0A S0B

4-to-1 MUX: truth table Select Data Out S1 S0 A B C D 1

4-to-1 MUX: gate version

Addresses 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

4-to-1 MUX: truth table (revisited) Select Data Out S1 S0 D0 D1 D2 D3 1

Demultiplexing one input is routed to one of several outputs Like mail may be sent to any number of recipients In addition to data input, there must be select inputs To select from 2N data outputs requires N select inputs Demultiplexer aka DeMUX

1-to-4 DeMux: Truth table Select Data Output S1 S0 A O0 O1 O2 O3 1

1-to-4 DeMUX: gate version

Decoder A variation on the previous circuit is to have no input data the selected output will be high, the others low This can be used to activate a control pin on the selected part of circuit

1-to-4 Decode: Truth table Select Output S1 S0 O0 O1 O2 O3 1

1-to-4 Decode: gates

Decoder plus registers = RAM Memory Address Register (MAR) holds an address associated with memory Memory Data Register (MDR) holds data for writing to memory Memory is a sequence of registers and a decoder Decoder output is connected to control pins (load in this example) of the RAM

Decoder plus registers = RAM Load pins MDR Decoder MAR

The logic of ROM fuse Address lines 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 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)