ECE124 D IGITAL C IRCUIT D ESIGN
Otman A. AL Basir (Basir)
Department of Electrical and Computer Engineering
University of Waterloo
Winter 2021
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R EVIEW : QM TABULATION M ETHOD
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R EVIEW : QM TABULATION M ETHOD
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R EVIEW : QM TABULATION M ETHOD
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R EVIEW : QM TABULATION M ETHOD
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R EVIEW : QM TABULATION M ETHOD
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R EVIEW : QM TABULATION M ETHOD
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R EVIEW : P ETRICK ’ S M ETHOD
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R EVIEW : P ETRICK ’ S M ETHOD
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P RIORITY E NCODERS
Priority Encoder – A priority encoder is an encoder circuit in which inputs
are processed for priorities. When more than one inputs are active at the
same time, the input with higher priority takes precedence and the output
corresponding to that input is generated.
Consider the 4-to-2 priority encoder as an example.
From the truth table, one can see that when all inputs are 0, the valid bit V is
zero and outputs are not used.
Let input D3 be the highest priority, therefore, regardless of the other inputs,
when D3 is high, the output has to be its binary code 11.
Let input D0 be the lowest priority, therefore the output would be 00 only when
D0 is high and the other input lines are low.
Similarly, D2 has higher priority over D1 and D0 but lower than D3 therefore the
output would be 010 only when D2 is high and D3 is low (D0 & D1 are don’t
care).
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P RIORITY E NCODER
Implementation – It can clearly be seen that the condition for valid bit to be 1 is
that at least any one of the inputs should be high.
Hence,V = D0 + D1 + D2 + D3
X = D2 + D3
Y = D1 D2’ + D3
Hence, the priority 4-to-2 encoder can be realized as follows:
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USING MUX IN MEMORY- MULTIDEVICE INTERFACING
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B UFFERS VS M UXS
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F UNCTION I MPLEMENTATION USING M UX
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F UNCTION I MPLEMENTATION USING M UX
2n−1 -to-1 multiplexer can implement any n variable function
n − 1 control variables; remaining variable is a data input to the mux.
Example F(A,B,C)=m0+m2+m6+m7; n=3; n-1=2, so let us use 4-to-1 mux
F(A,B,C)=A’.B’.C’+A’.B.C’+A.B.C’+A.B.C. Let us use A,B as the control
variables, C as the input variable
so we have: m0=(A’B’.C’); A’B’-control select line 0, thus we connect line 0 to
C’.
m2=(A’.B.C’); A’.B-control select line 1, thus we connect line 1 to C’.
we have m6=(A.B.C’); A.B-conrol select line 3, thus we connect line 3 to C’
we have m7=(A,B,C); A.B-control select line 3, thus we connect line 3 to C.
Thus we realize line 3 is 1 regardless of C, line 3 is connected to 1.
all control conditions are covered (A’.B’), (A’.B),(A,B), except for (A.B’),
thus this control value is not presnet in any min term, as a result we
connect this line to zero
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F UNCTION I MPLEMENTATION USING M UX
The same relaization can be derived from the truth table, where A and B
are considered as control variables, C as an input variable.
A B C F F
0 0 0 1 C’
0 0 1 0
0 1 0 1 C’
0 1 1 0
1 0 0 0 0
1 0 1 0
1 1 0 1 1
1 1 1 1
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U SING D ECODERS
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U SING D ECODERS
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