CSCI 320 — Introducing Logisim

This is a lab experience. There will be no grade for this lab.

It is mostly to give those who did not use Logisim last semester, a chance to refresh their skills.

If you’ve never used Logisim or have forgotten everything you know about it, you should review Tasks 1 to 4 of the CSCI 255 Introducing Logisim lab.

The truth table of interest

Here’s the truth table for a modulo-3 adder. Notice the use of don’t cares.


In this implementation numbers from 0 to 2 are encoded in binary as two bits 0b00 to 0b10 (using the Java 7 notation). We are assuming the 3, 0b11, never occurs. This allows us to use don’t cares for 7 of the 16 possible input combinations.

In the usual digital logic notation, this can be expressed as follows:

Stuff to do

First, using Karnaugh maps, derive a boolean expression to implement the modulo-3 adder.

Second, start up Logisim and use the circuit analyzer to implement this boolean expression in a subcircuit called Add3. Start by defining input pins A1, A0, B1, B0 and output pins for S1 and S0 in your subcircuit. Then use the Analyze Circuit feature of Logisim to generate the circuit. (See Task 4 of the Introducing Logisim lab for more information.)

Third, use the almost-impossible-to-use splitters of Logisim to modify your circuit so that its input is two pairs of wires, called in0 and in1, and its output is one pair of wires, called out. Be sure to change the pins to have a data width of two.

Fourth, make a new subcircuit called Inc3. The subcircuit Inc3 should have a input port called in and an output port called out. Both will have a data width of two. Inc3 receives a two-bit input and increments it modulo-3. This means in Java-speak that Inc3(x) is something like Add3(x,1). Do not just copy your implementation of Add3 to Inc3. Use Add3 as a subcomponent, just as you would have one method call another in Java. All you have to do is “pass” a constant 1.

Fifth, make a third subcircuit called Count3. This circuit will have a clock input port clock. and an output port called out. On clock ticks, this ciruit will count from 0 to 2 using modulo-3 addition (0,1,2,0,1,2,0,1,2, …). Count3 should be built with a two-bit register and an single “instance” of Inc3. There’s really only one legal way to wire these two components together.