Exercise DET-05.08 – From the energy manager to the hot water (Solution)

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

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

Task

In our example system, the energy manager tells the heat pump over the two switching signals $A$ and $B$ of Smart Grid Ready (SG Ready) what it wants: block (1:0), normal operation (0:0) or boost (0:1). The controller turns the two signals into its operating states. In simplified form, you follow this path from the energy manager to the hot water.

The energy manager has three inputs, of which exactly one is to be 1: $I_0$ for normal operation, $I_1$ for boost and $I_2$ for block. Its encoder delivers the outputs $E_A$ and $E_B$, which drive the signals $A$ and $B$.

a) Design the encoder: set up the truth table with don’t cares, and give the minimized expressions of $E_A$ and $E_B$.

b) By mistake, block and boost are requested at the same time. What does your encoder send, and what would this code word mean?

c) Change the encoder so that block has priority over boost, and $E_A$ and $E_B$ can never be 1 at the same time. Give the expressions.

The controller side is given as a simulation. A 2-to-4 decoder with a lockout forms the outputs $Y_0$ (normal operation), $Y_1$ (boost) and $Y_{\mathrm{block}}$, as in the lesson. In boost, the hot water is heated to the upper set point of 54.0 °C instead of the normal 52.5 °C; multiplexers with the select input $Y_1$ choose between the two set points. For the hot water, the input $D$ is the hot-water demand. It is passed on as $W$ only if there is no block. A 1-to-2 demultiplexer routes $W$ to the heat pump that is defined for hot water: to $H_1$ for $S=0$ and to $H_2$ for $S=1$.

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="96 96 96 48" f="2"/>
  <L x="144 96 144 48" f="2" p="1"/>
  <I x="208 128 272 128" f="0" sl="0.5" hi="5"/>
  <I x="208 176 272 176" f="0" sl="0.5" hi="5"/>
  <And x="432 320 576 320" f="0"/>
  <And x="432 384 576 384" f="0" o="5"/>
  <And x="432 448 576 448" f="0"/>
  <And x="432 512 576 512" f="0"/>
  <Or x="784 608 928 608" f="0"/>
  <M x="1024 352 1072 352" f="2"/>
  <M x="1024 480 1072 480" f="2"/>
  <M x="1024 608 1072 608" f="2"/>
  <I x="992 704 1056 704" f="0" sl="0.5" hi="5"/>
  <And x="1152 720 1296 720" f="0"/>
  <L x="1104 736 1056 736" f="2"/>
  <dmux x="1360 720 1456 720" f="0" se="1"/>
  <M x="1328 704 1328 656" f="2"/>
  <L x="1392 864 1392 912" f="2"/>
  <M x="1504 720 1552 720" f="2"/>
  <M x="1504 752 1552 752" f="2"/>
  <w x="96 128 208 128" f="0"/>
  <w x="96 432 432 432" f="0"/>
  <w x="96 496 432 496" f="0"/>
  <w x="96 96 96 128" f="0"/>
  <w x="96 128 96 432" f="0"/>
  <w x="96 432 96 496" f="0"/>
  <w x="272 128 320 128" f="0"/>
  <w x="320 304 432 304" f="0"/>
  <w x="320 368 432 368" f="0"/>
  <w x="320 128 320 304" f="0"/>
  <w x="320 304 320 368" f="0"/>
  <w x="144 176 208 176" f="0"/>
  <w x="144 400 432 400" f="0"/>
  <w x="144 528 432 528" f="0"/>
  <w x="144 96 144 176" f="0"/>
  <w x="144 176 144 400" f="0"/>
  <w x="144 400 144 528" f="0"/>
  <w x="272 176 368 176" f="0"/>
  <w x="368 336 432 336" f="0"/>
  <w x="368 464 432 464" f="0"/>
  <w x="368 176 368 336" f="0"/>
  <w x="368 336 368 464" f="0"/>
  <w x="576 320 624 320" f="0"/>
  <w x="624 352 928 352" f="0"/>
  <w x="624 320 624 352" f="0"/>
  <w x="928 352 1024 352" f="0"/>
  <w x="576 384 656 384" f="0"/>
  <w x="656 480 928 480" f="0"/>
  <w x="656 384 656 480" f="0"/>
  <w x="928 480 1024 480" f="0"/>
  <w x="576 448 688 448" f="0"/>
  <w x="688 592 784 592" f="0"/>
  <w x="688 448 688 592" f="0"/>
  <w x="576 512 720 512" f="0"/>
  <w x="720 624 784 624" f="0"/>
  <w x="720 512 720 624" f="0"/>
  <w x="928 608 960 608" f="0"/>
  <w x="960 608 1024 608" f="0"/>
  <w x="960 608 960 704" f="0"/>
  <w x="960 704 992 704" f="0"/>
  <w x="1056 704 1152 704" f="0"/>
  <w x="1104 736 1152 736" f="0"/>
  <w x="1296 720 1328 720" f="0"/>
  <w x="1328 720 1360 720" f="0"/>
  <w x="1328 704 1328 720" f="0"/>
  <w x="1392 816 1392 864" f="0"/>
  <w x="1456 720 1504 720" f="0"/>
  <w x="1456 752 1504 752" f="0"/>
  <x x="91 20 101 23" f="0" si="16" te="A"/>
  <x x="139 20 149 23" f="0" si="16" te="B"/>
  <x x="326 122 336 125" f="2" si="16" te="A"/>
  <x x="374 170 384 173" f="2" si="16" te="B"/>
  <x x="1092 358 1164 361" f="0" si="16" te="Y0 normal"/>
  <x x="1092 486 1155 489" f="0" si="16" te="Y1 boost"/>
  <x x="1092 614 1144 617" f="0" si="16" te="Y block"/>
  <x x="904 742 1048 745" f="0" si="16" te="D hot-water demand"/>
  <x x="1340 662 1355 665" f="0" si="16" te="W"/>
  <x x="1412 918 1613 921" f="0" si="16" te="S: heat pump 2 for hot water"/>
  <x x="1572 726 1765 729" f="0" si="16" te="H1: heat pump 1, hot water"/>
  <x x="1572 758 1765 761" f="0" si="16" te="H2: heat pump 2, hot water"/>
</cir>

d) Fill in the gaps for the signals $A$ and $B$. Check the outputs of the decoder in the simulation.

$A$	$B$	Code word means	$Y_0$	$Y_1$	$Y_{\mathrm{block}}$	Selected set point
0	0	normal operation	1	0	0	52.5 °C
0	1	boost			0
1	0	block	0
1	1	start command, locked out

e) Fill in the gaps for the hot water. Check your table in the simulation.

Row	$A$	$D$	$S$	$W$	$H_1$	$H_2$
0	0	0	0	0	0	0
1	0	0	1
2	0	1	0	1
3	0	1	1		0	1
4	1	0	0
5	1	0	1	0	0
6	1	1	0			0
7	1	1	1		0

f) In which rows does a heat pump go on heating the house while the other one heats the hot water? In which rows does neither of them receive a demand, even though $D=1$, and why?

◀️ Back to the task

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Solution

Given

Given explicitly:

• the code words of Smart Grid Ready (SG Ready): block 1:0, normal operation 0:0, boost 0:1
• the encoder with the inputs $I_0$, $I_1$ and $I_2$, of which exactly one is 1, and the outputs $E_A$ and $E_B$
• the controller side as a simulation: decoder with a lockout, the block in front of the demultiplexer
• the set points 52.5 °C and 54.0 °C, and multiplexers with the select input $Y_1$ that choose between them
• the demultiplexer: $H_1$ for $S=0$, $H_2$ for $S=1$

Known:

• SG Ready with a lockout (DET-05)
• The encoder, don’t cares, and the priority encoder (DET-05)
• Multiplexer and demultiplexer (DET-05, DET-05)
• The hot water in the cascade with partial priority (DET-05)

Required

a) the truth table and the expressions of the encoder
b) what the encoder sends for block and boost at the same time, and what it means
c) the expressions with block having priority
d) the complete table for $A$ and $B$
e) the complete table for the hot water
f) the rows in which one heat pump goes on heating, and those in which the block stops the demand

a) The encoder

Exactly one input is 1, so only three rows are specified; the other rows never occur and become don’t cares, marked X, as in the encoder of the lesson (DET-05, 4.1):

Row	$I_2$	$I_1$	$I_0$	Wanted	$E_A$	$E_B$
0	0	0	0	–	X	X
1	0	0	1	normal operation	0	0
2	0	1	0	boost	0	1
3	0	1	1	–	X	X
4	1	0	0	block	1	0
5	1	0	1	–	X	X
6	1	1	0	–	X	X
7	1	1	1	–	X	X

The don’t cares allow the largest loops. $E_A$ has its only 1 in row 4, and the loop may grow over the don’t cares up to all rows with $I_2=1$. $E_B$ has its only 1 in row 2, and the loop may grow to all rows with $I_1=1$:

$$\begin{array}{rl}{E}_A(I_2,I_1,I_0)& =\sum m(4)+d(0,3,5,6,7)=I_2\\ E_B(I_2,I_1,I_0)& =\sum m(2)+d(0,3,5,6,7)=I_1\end{array}$$

The input $I_0$ is not needed, because its code word is 0:0 (DET-05, 4.1). The encoder has no input for the start command either: this is the lockout at the transmitter.

b) Block and boost at once

With $I_2=1$ and $I_1=1$, both outputs become 1: $E_A=1$ and $E_B=1$. The encoder sends the code word 1:1, the start command (DET-05, 3.2). This is exactly the code word that must never act in our system. As long as exactly one input is 1, it does not occur; as soon as block and boost coincide, it does.

c) Block with priority

A priority encoder encodes only the active input with the highest priority (DET-05, 4.1). Block has priority, so $E_B$ may be 1 only without a block:

$$\begin{array}{rl}{E}_A& =I_2\\ E_B& =I_1\cdot \overline{I_2}\end{array}$$

Now every row of the table is defined, and row 6, with block and boost at once, gives the code word 1:0:

Row	$I_2$	$I_1$	$I_0$	$E_A$	$E_B$
0	0	0	0	0	0
1	0	0	1	0	0
2	0	1	0	0	1
3	0	1	1	0	1
4	1	0	0	1	0
5	1	0	1	1	0
6	1	1	0	1	0
7	1	1	1	1	0

The two outputs are never 1 at the same time, so the start command cannot occur any more ✓

d) From the two signals to the set point

Each output of the decoder is 1 for its code word, and the OR gate leads 1:1 into the block (DET-05, 3.2):

$$\begin{array}{rl}{Y}_0& =\overline{A}\cdot \overline{B}\\ Y_1& =\overline{A}\cdot B\\ Y_{\mathrm{block}}& =A\cdot \overline{B}+A\cdot B=A\end{array}$$

The select input of the multiplexers is $Y_1$. So they pass the upper set point only in boost, and the normal set point otherwise (DET-05, 5.1):

$A$	$B$	Code word means	$Y_0$	$Y_1$	$Y_{\mathrm{block}}$	Selected set point
0	0	normal operation	1	0	0	52.5 °C
0	1	boost	0	1	0	54.0 °C
1	0	block	0	0	1	52.5 °C
1	1	start command, locked out	0	0	1	52.5 °C

In the rows with $A=1$, the multiplexers pass the normal set point, because $Y_1=0$. In this simplified circuit, it has no effect there: the block stops the demand, as e) shows.

e) The hot water

The block stops the demand, and the demultiplexer routes what remains (DET-05, 5.2):

$$\begin{array}{rl}W& =D\cdot \overline{A}\\ H_1& =\overline{S}\cdot W\\ H_2& =S\cdot W\end{array}$$

Row	$A$	$D$	$S$	$W$	$H_1$	$H_2$
0	0	0	0	0	0	0
1	0	0	1	0	0	0
2	0	1	0	1	1	0
3	0	1	1	1	0	1
4	1	0	0	0	0	0
5	1	0	1	0	0	0
6	1	1	0	0	0	0
7	1	1	1	0	0	0

f) Reading the table

In the rows 2 and 3, there is a demand without a block. The demultiplexer starts the hot-water operation of the heat pump that $S$ selects. The heat pump whose output stays 0 remains free for the heating: the partial priority of the lesson (DET-05, 5.2).

In the rows 6 and 7, there is a demand as well, but $A=1$ means a block, so $W=0$, and neither heat pump receives the demand.