1 of 6

7-Segment LASACS

Objectives

Use Logisim to spell out L A S A C S on a 7-segment display using (a) straight forward SOP (b) partially simplified (c) and DeMorgan logic

2 of 6

7-segment in Logisim

3 of 6

Circuit drawing suggestion

Your

circuit

here

Put your inputs on the top and then have vertical wires for them and their inversions, then it's really easy to get the signal (or it's inversion) and use it in your circuit using horizontal wires.

4 of 6

LASACS (Sum of Products)

Fill out the Truth Table assuming a common cathode 7-segment
In logisim, for each of the outputs a - g, implement a sum of products (SOP) circuit like the one shown here & connect the outputs to a 7-segment display. Reuse gates - i.e. don't duplicate gates that do the same thing.
If a segment is always ON or OFF simply connect it to Power or GND (in Logisim's Wiring menu)

x	y	z		a	b	c	d	e	f	g
0	0	0	L
0	0	1	A
0	1	0	S
0	1	1	A
1	0	0	C
1	0	1	S

Your circuit should have 102 transistors

do it all in one circuit (don't use any subcircuits)

You should end up with a circuit with 6 AND gates and 5 OR gates.

5 of 6

LASACS (Partially Simplified)

Look at the truth table on the previous page and implement simplified logic for each segment¹ to get the LASACS (Partially Simplified) circuit. In addition to the 3 inverters to invert the 3 inputs, your circuit can only have AND and OR gates (i.e. no NAND or NOR gates).

Start with

these should be

the only inverters

in your circuit

segment e

HINT Except for e, none of the other segment requires more than one logic gate (most with only 2 inputs).

How many transistors does your circuit have? put # of transistors label on your circuit

use the text tool to label each gate connected to the 7-seg display with the segment name.

build it all in one circuit (don't use any subcircuits)

¹do not optimize by combining logic for different segments, except if the gate goes directly to a segment

6 of 6

LASACS (DeMorgan's)

Make a copy of your LASACS (Partially Simplified) circuit and apply DeMorgan's to each of the gates directly connected to the 7 segment display to reduce the number of transistors in the circuit. Each segment a-g should now be connected to a NAND or NOR gate or power/gnd. Label each gate connected to a segment with its segment name.

Get your circuit to 42 or less transistors¹.

How many transistors does your circuit have? put # of transistors label on your circuit

after DeMorgan's lecture

¹if you combine & optimize further it can be done in as few as 24 transistors