Exercise DET-05.05 – Analysis of given multiplexer and demultiplexer circuits

Prof. Dr. Thorsten Jungmann (last updated 2026-11-02)

Relates to DET-05 Codes, code converters and standard components

Task

The three circuits below are drawn according to the standard of the International Electrotechnical Commission (IEC), IEC 60617. In each of them, follow the select inputs to find out what the multiplexers and demultiplexers do, and then fill in the gaps in the truth table. In the symbols, the data inputs and outputs carry their numbers; the data input with the number $k$ is called $I_{k}$ below.

Circuit 1 has the inputs $A$ , $B$ and $C$ and the output $F$ .

Circuit 1 according to IEC 60617: a 4-to-1 multiplexer with the select inputs B and A and the data inputs C, C bar, 1 and 0, which drives the output F

a) Fill in the gaps.

Row	$A$	$B$	$C$	Selected data input	$F$
0	0	0	0	$I_{0}$	0
1	0	0	1
2	0	1	0		1
3	0	1	1	$I_{1}$
4	1	0	0
5	1	0	1	$I_{2}$
6	1	1	0		0
7	1	1	1

Check your truth table of a) in the simulation of circuit 1.

Simulation of circuit 1 with a 4-to-1 multiplexer, in which all inputs A, B and C are low and the output F is low

Open in the simulator

Circuit as text (File → Import From Text…)

<cir f="1" ts="0.000005" ic="1.500424758475255" cb="50" pb="50" vr="5" mts="5e-11">
  <L x="416 368 416 416" f="2"/>
  <L x="384 464 384 512" f="2"/>
  <L x="96 160 48 160" f="2"/>
  <mux x="320 160 448 160" f="0" se="2"/>
  <I x="176 192 240 192" f="0" sl="0.5" hi="5"/>
  <L x="320 224 272 224" f="2" p="1"/>
  <L x="320 256 272 256" f="2"/>
  <M x="448 160 496 160" f="2"/>
  <w x="416 320 416 368" f="0"/>
  <w x="384 320 384 464" f="0"/>
  <w x="96 160 144 160" f="0"/>
  <w x="144 160 320 160" f="0"/>
  <w x="144 160 144 192" f="0"/>
  <w x="144 192 176 192" f="0"/>
  <w x="240 192 320 192" f="0"/>
  <x x="436 422 446 425" f="0" si="16" te="A"/>
  <x x="404 518 414 521" f="0" si="16" te="B"/>
  <x x="16 166 27 169" f="0" si="16" te="C"/>
  <x x="516 166 525 169" f="0" si="16" te="F"/>
  <x x="324 136 447 139" f="0" si="16" te="4-to-1 multiplexer"/>
</cir>

b) Give the minterm list of $F$ , and a disjunctive normal form (DNF) that follows directly from the data inputs.

Circuit 2 has the inputs $A$ , $B$ and $C$ and the outputs $Y_{0}$ to $Y_{3}$ and $Z$ .

Circuit 2 according to IEC 60617: a 1-to-4 demultiplexer with the select inputs B and A and the input C, the outputs Y0 to Y3, and an OR gate over Y1 and Y2 with the output Z

c) Fill in the gaps.

Row	$A$	$B$	$C$	$Y_{0}$	$Y_{1}$	$Y_{2}$	$Y_{3}$	$Z$
0	0	0	0	0	0	0	0	0
1	0	0	1			0	0
2	0	1	0			0	0	0
3	0	1	1	0		0	0
4	1	0	0	0	0	0	0
5	1	0	1	0	0		0
6	1	1	0	0	0	0		0
7	1	1	1	0	0	0

Check your truth table of c) in the simulation of circuit 2.

Simulation of circuit 2 with a 1-to-4 demultiplexer and an OR gate, in which all inputs are low and all outputs are low

Open in the simulator

Circuit as text (File → Import From Text…)

<cir f="1" ts="0.000005" ic="1.500424758475255" cb="50" pb="50" vr="5" mts="5e-11">
  <L x="384 368 384 416" f="2"/>
  <L x="352 464 352 512" f="2"/>
  <dmux x="320 160 448 160" f="0" se="2"/>
  <L x="320 160 272 160" f="2"/>
  <M x="592 160 640 160" f="2"/>
  <M x="592 192 640 192" f="2"/>
  <M x="592 224 640 224" f="2"/>
  <M x="592 256 640 256" f="2"/>
  <Or x="592 416 736 416" f="0"/>
  <M x="784 416 832 416" f="2"/>
  <w x="384 320 384 368" f="0"/>
  <w x="352 320 352 464" f="0"/>
  <w x="448 160 592 160" f="0"/>
  <w x="448 192 512 192" f="0"/>
  <w x="512 192 592 192" f="0"/>
  <w x="512 192 512 400" f="0"/>
  <w x="512 400 592 400" f="0"/>
  <w x="448 224 480 224" f="0"/>
  <w x="480 224 592 224" f="0"/>
  <w x="480 224 480 432" f="0"/>
  <w x="480 432 592 432" f="0"/>
  <w x="448 256 592 256" f="0"/>
  <w x="736 416 784 416" f="0"/>
  <x x="404 422 414 425" f="0" si="16" te="A"/>
  <x x="372 518 382 521" f="0" si="16" te="B"/>
  <x x="240 166 251 169" f="0" si="16" te="C"/>
  <x x="660 166 679 169" f="0" si="16" te="Y0"/>
  <x x="660 198 679 201" f="0" si="16" te="Y1"/>
  <x x="660 230 679 233" f="0" si="16" te="Y2"/>
  <x x="660 262 679 265" f="0" si="16" te="Y3"/>
  <x x="852 422 861 425" f="0" si="16" te="Z"/>
  <x x="324 136 465 139" f="0" si="16" te="1-to-4 demultiplexer"/>
</cir>

d) Give the logic expression of $Z$ . For which inputs is $Z = 1$ ? Say it in one sentence.

Circuit 3 sends four fixed data inputs over one line $L$ . It has the inputs $S_{1}$ , $S_{0}$ , $T_{1}$ and $T_{0}$ and the outputs $L$ and $Q_{0}$ to $Q_{3}$ .

Circuit 3 according to IEC 60617: a 4-to-1 multiplexer with the select inputs S0 and S1 and the data inputs 1, 0, 1 and 1 drives a single line L into a 1-to-4 demultiplexer with the select inputs T0 and T1 and four outputs

e) Fill in the gaps.

$S_{1}$	$S_{0}$	$T_{1}$	$T_{0}$	$L$	$Q_{0}$	$Q_{1}$	$Q_{2}$	$Q_{3}$
0	0	0	0	1	1	0	0	0
0	1	0	1				0	0
1	0	1	0	1	0	0		0
1	1	1	1		0	0	0
0	0	1	0			0		0
0	1	0	0			0	0	0
1	1	0	1	1	0		0	0
1	0	1	1		0	0	0

Check your truth table of e) in the simulation of circuit 3.

Simulation of circuit 3 with a 4-to-1 multiplexer and a 1-to-4 demultiplexer over one line, in which the select inputs are low and the line L and the output Q0 are high

Open in the simulator

Circuit as text (File → Import From Text…)

<cir f="1" ts="0.000005" ic="1.500424758475255" cb="50" pb="50" vr="5" mts="5e-11">
  <L x="352 368 352 416" f="2"/>
  <L x="320 464 320 512" f="2"/>
  <L x="640 368 640 416" f="2"/>
  <L x="608 464 608 512" f="2"/>
  <mux x="256 160 384 160" f="0" se="2"/>
  <dmux x="576 160 704 160" f="0" se="2"/>
  <L x="256 160 208 160" f="2" p="1"/>
  <L x="256 192 208 192" f="2"/>
  <L x="256 224 208 224" f="2" p="1"/>
  <L x="256 256 208 256" f="2" p="1"/>
  <M x="480 144 480 96" f="2"/>
  <M x="752 160 800 160" f="2"/>
  <M x="752 192 800 192" f="2"/>
  <M x="752 224 800 224" f="2"/>
  <M x="752 256 800 256" f="2"/>
  <w x="352 320 352 368" f="0"/>
  <w x="320 320 320 464" f="0"/>
  <w x="640 320 640 368" f="0"/>
  <w x="608 320 608 464" f="0"/>
  <w x="384 160 480 160" f="0"/>
  <w x="480 160 576 160" f="0"/>
  <w x="480 144 480 160" f="0"/>
  <w x="704 160 752 160" f="0"/>
  <w x="704 192 752 192" f="0"/>
  <w x="704 224 752 224" f="0"/>
  <w x="704 256 752 256" f="0"/>
  <x x="372 422 391 425" f="0" si="16" te="S1"/>
  <x x="340 518 359 521" f="0" si="16" te="S0"/>
  <x x="660 422 678 425" f="0" si="16" te="T1"/>
  <x x="628 518 646 521" f="0" si="16" te="T0"/>
  <x x="500 102 508 105" f="0" si="16" te="L"/>
  <x x="820 166 841 169" f="0" si="16" te="Q0"/>
  <x x="820 198 841 201" f="0" si="16" te="Q1"/>
  <x x="820 230 841 233" f="0" si="16" te="Q2"/>
  <x x="820 262 841 265" f="0" si="16" te="Q3"/>
</cir>

f) Under which condition does each output $Q_{k}$ show exactly its own data input $I_{k}$ , and what happens otherwise? How would you have to drive the select inputs for all four signals to share the line $L$ ?

Solution

a) $F$ is 1 in rows 1, 2, 4 and 5, 0 in all others
b) $F (A, B, C) = \sum m (1, 2, 4, 5)$ ; $F = \overline{A} \cdot \overline{B} \cdot C + \overline{A} \cdot B \cdot \overline{C} + A \cdot \overline{B}$
c) $Y_{k}$ equals $C$ for the $k$ that $A$ and $B$ select, the other outputs are 0; $Z$ is 1 in rows 3 and 5
d) $Z = (A \oplus B) \cdot C$ ; $Z = 1$ if $C = 1$ and $A$ and $B$ differ
e) $L$ shows the data input that $S_{1}$ and $S_{0}$ select, $Q_{k}$ shows $L$ for the $k$ that $T_{1}$ and $T_{0}$ select, the other outputs are 0
f) only if both pairs of select inputs carry the number $k$ ; otherwise, the signal of the selected data input arrives at the output that $T_{1}$ and $T_{0}$ select, which then shows a foreign signal; for sharing, both pairs have to run through the numbers 0 to 3 together

▶️ Full worked solution

Wattsinside

Exercise DET-05.05 – Analysis of given multiplexer and demultiplexer circuits

Task

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