digital logic problems
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Digital Logic Problems (II)
Prof. Sin-Min Lee
Department of Mathematics andComputer Science
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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”.
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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.
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• 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). .
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• 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*
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• 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.
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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.
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Multiplexers (continued)• S0 and S1 are the selection inputs.
• D0, D1, D2, D3 are the input lines.
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Multiplexers (continued)• MUX blocks can be combined in parallel with common
selection and enable inputs to perform selection on multiple
bit quantities.
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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.
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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.
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Example of MUX combo circuit• F(X,Y,Z) = Sm(1,2,6,7)
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Implement g(w,x,y)=wx+xy+wy using a 4-1 multiplexer.
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