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.
| inputs | outputs | ||||
|---|---|---|---|---|---|
| a1 | a0 | b1 | b0 | s1 | s0 |
| 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 1 |
| 0 | 0 | 1 | 0 | 1 | 0 |
| 0 | 0 | 1 | 1 | x | x |
| 0 | 1 | 0 | 0 | 0 | 1 |
| 0 | 1 | 0 | 1 | 1 | 0 |
| 0 | 1 | 1 | 0 | 0 | 0 |
| 0 | 1 | 1 | 1 | x | x |
| 1 | 0 | 0 | 0 | 1 | 0 |
| 1 | 0 | 0 | 1 | 0 | 0 |
| 1 | 0 | 1 | 0 | 0 | 1 |
| 1 | 0 | 1 | 1 | x | x |
| 1 | 1 | 0 | 0 | x | x |
| 1 | 1 | 0 | 1 | x | x |
| 1 | 1 | 1 | 0 | x | x |
| 1 | 1 | 1 | 1 | x | x |
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:
- s1(a1,a0,b1,b0) = Σ(2,5,8) + d(3,7,11,12,13,14,15)
- s0(a1,a0,b1,b0) = Σ(1,4,10) + d(3,7,11,12,13,14,15)
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