Exercise DET-05.03 – Floor indicator of a lift

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

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

Task

The cabin of a lift shows the floor on a 7-segment display. In a building with the floors 0 to 7, the controller of the lift delivers the floor as a binary code word with the bits $A$, $B$ and $C$, $A$ with the weight 4. A code converter turns this code word into the seven segment signals $Y_a$ to $Y_g$; each of them is 1 when its segment lights up. The figure shows which segments form which digit, and the truth table gives the same code as bits.

Floor	$A$	$B$	$C$	$Y_a$	$Y_b$	$Y_c$	$Y_d$	$Y_e$	$Y_f$	$Y_g$
0	0	0	0	1	1	1	1	1	1	0
1	0	0	1	0	1	1	0	0	0	0
2	0	1	0	1	1	0	1	1	0	1
3	0	1	1	1	1	1	1	0	0	1
4	1	0	0	0	1	1	0	0	1	1
5	1	0	1	1	0	1	1	0	1	1
6	1	1	0	1	0	1	1	1	1	1
7	1	1	1	1	1	1	0	0	0	0

a) Minimize $Y_a$ with a Karnaugh map.

b) Minimize $Y_d$ with a Karnaugh map.

c) Minimize $Y_g$ with a Karnaugh map. Is your result unique?

The other four segments are minimized in the same way, with these results:

• $Y_b=\overline{A}+B\cdot C+\overline{B}\cdot \overline{C}$
• $Y_c=A+\overline{B}+C$
• $Y_e=\overline{A}\cdot \overline{C}+B\cdot \overline{C}$
• $Y_f=A\cdot \overline{B}+A\cdot \overline{C}+\overline{B}\cdot \overline{C}$

d) Which product terms occur in the results of more than one segment? How many AND gates does the code converter need if it shares these terms between its segments, and how many if it does not?

e) Draw the part of the circuit that forms $Y_d$ and $Y_e$ according to the standard of the International Electrotechnical Commission (IEC), IEC 60617, with shared AND gates.

f) Check your results for floor 5: which segments light up, and does the digit agree with the truth table?

Solution

a) $Y_a=B+A\cdot C+\overline{A}\cdot \overline{C}$
b) $Y_d=\overline{A}\cdot B+\overline{A}\cdot \overline{C}+B\cdot \overline{C}+A\cdot \overline{B}\cdot C$
c) $Y_g=\overline{A}\cdot B+A\cdot \overline{B}+B\cdot \overline{C}$; not unique: $Y_g=\overline{A}\cdot B+A\cdot \overline{B}+A\cdot \overline{C}$ is just as small
d) in more than one segment: $\overline{A}\cdot \overline{C}$, $\overline{B}\cdot \overline{C}$, $\overline{A}\cdot B$, $B\cdot \overline{C}$ and $A\cdot \overline{B}$; 9 AND gates with shared terms, 16 without
e) three inverters; four AND gates for the terms of $Y_d$, two of which $Y_e$ uses as well; an OR gate with four inputs for $Y_d$ and one with two inputs for $Y_e$
f) the segments a, c, d, f and g light up, the digit 5, as in the truth table

▶️ Full worked solution