digital logic problems

8/10/2019 Digital logic problems

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Digital Logic Problems (II)

Prof. Sin-Min Lee

Department of Mathematics andComputer Science



Multiplexers

• A combinational circuit that selects info

from one of many input lines and directs it

to the output line.

• The selection of the input line is controlled

by input variables called selection inputs.

• They are commonly abbreviated as “MUX”.



Implementing Boolean

functions with multiplexers

• Any Boolean function of n variables can beimplemented with 2n -1-to-1 multiplexer. The

procedure for implementing a Boolean functionwith a multiplexer is

• 1.Express the function in its sum of mintermsform.

• 2. Order the sequence of variables chosen for theminterms. Suppose the sequence is , where A isthe leftmost variable, and are the remaining n -1variables.



• 3.Connect the n -1 variables to the selection lines

of the 2n -1-to-1 multiplexer, with B connected to

the highest order selection line, and so on.• 4. Construct the implementation table: List all the

minterms in two rows.

• The first row consists of minterms 0 to 2n -1 -1 (in all of

which A is complemented).

• The second row consists of minterms 2n -1 to 2n -1 (in all

of which A is uncomplemented). .



• 5. Circle all the minterms of the function andinspect each column in the implementation tableseparately

• If the two minterms in a column are not circled, apply 0to the corresponding multiplexer input.

• If the two minterms are circled, apply 1 to thecorresponding multiplexer input.

• If the bottom minterm is circled, and the top is notcircled, apply A to the corresponding multiplexer input.

• If the top minterm is circled but not the bottom, applyA*



• Multiplexers and decoders are used when many

lines of information are being gated and passed

from one part of a circuit to another.• Multiplexing is when multiple data signals share a

common propagation path. Time multiplexing is

when different signals travel along the same wire

but at different times. These devices have data andaddress lines, and usually include an enable/

disable input. When the device is disabled the

output is locked into some particular state and is

not effected by the inputs.



Consider the function of 3 variables:

1. Input variables B and C are applied to the selection lines s 1 and s 0,

respectively.

2. Construct the implementation table, and circle all the minterms of thfunction in the implementation table

3. Apply 0, 1, A , and

A* to the inputs I 0

through I 3.



Multiplexers (continued)• S0 and S1 are the selection inputs.

• D0, D1, D2, D3 are the input lines.



Multiplexers (continued)• MUX blocks can be combined in parallel with common

selection and enable inputs to perform selection on multiple

bit quantities.



Combinational circuit

implementation using MUX• We can use Multiplexers to express

Boolean functions also.

• Expressing Boolean functions as MUXs

is more efficient than as decoders.

• First n-1 variables of the function used

as selection inputs; last variable used as

data inputs.• If last variable is called Z, then each

data input has to be Z, Z’, 0, or 1.



Karnaugh Map Method of Multiplexer Implementation

Consider the function:

A is taken to be the data variable and B,C to be the select variables.



Example of MUX combo circuit• F(X,Y,Z) = Sm(1,2,6,7)



Implement g(w,x,y)=wx+xy+wy using a 4-1 multiplexer.

digital logic problems

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