Lab 3 Splitters, Adders and ALUs

CSC258 - Lab 3
Splitters, Adders and ALUs
1 Learning Objectives
In this lab you will design (a) multiplexers using the splitter component, (b) a simple ripple-carry adder,
and (c) an Arithmetic Logic Unit (ALU), a fundamental component of each processor. You will also gain
more practice with hierarchical design in Logisim and with using binary and hexadecimal numbers.
2 Marking Scheme
This lab is also worth 6% of your final grade, but you will be graded out of 8 marks for this lab, as
follows.
• Prelab + Test Vectors: 3 marks
• Part I : 1 mark
• Part II : 1 mark
• Part III : 3 marks
3 Preparation Before the Lab
Carefully review the “Preparation Before the Lab” instructions in the Lab 2 handout.
You are required to complete Parts I to III of the lab by building and testing your circuit in Logisim.
Include your schematics and circuit in Logisim for Parts I to III in the prelab. You must test your circuit
in Logisim using reasonable test vectors written in the format described in Lab 1 and Lab 2 handouts.
The term test vector simply refers to one combination of inputs that you will use to test your design. Each
simulation should consist of multiple test vectors, sufficient to demonstrate that your design functions
as intended. Make sure to submit these test vector files as well.
You are also recommended to find information about Wiring in logisim reference.pdf. Wiring components
will be useful for this lab.
You are required to implement and test all of Parts I to III of the lab. You need to show your designs
and demonstrate the operation of each part to the teaching assistants, including your test vectors.
4 Part I
For this part of the lab, you will learn how to use Splitter ( ) to divide a multi-bit value into individual
bits. These bits in turn will become the input signals to a 7-to-1 multiplexer that you create.
Generally, multi-bit values are used as a single unit to store integers or other data values. At times
though, these multi-bit values are just a grouping of related individual bits. When this is the case, we
often need to split up these bits and send them in different directions. We can accomplish this with
the Splitter component. The Splitter can be found under Wiring in components. You can find more
information about this component in Help > User’s Guide > Additional Features > Splitters.
In addition to splitting multi-bit values into individual bits, splitters can also be used to concatenate
individual bits into a single multi-bit value. You can adjust the multi-bit width, the ”fan out” number
and the direction of the splitter in its properties.
1
For this part, the splitter will be used to provide inputs to a 7-to-1 multiplexer that you will create in
Logisim. In the components list, find and select Plexers > Multiplexer and then add one to the canvas.
Clicking on the multiplexer you just created, go to Properties at the bottom left of the screen, change
Select Bits to a value that allows 7 data inputs for your multiplexer.
1. Before implementing this on Logisim, draw a schematic that shows how a multi-bit input would be
split up to provide inputs to a 7-to-1 multiplexer. Draw your schematic (how your overall design
breaks down into interconnected modules) and label all inputs, outputs and wires between modules.
Be prepared to explain your design approach to the TA as part of your preparation. (PRELAB)
(a) Assume that at the highest level, the multi-bit input is coming from the DE1-SOC switches
(with the first data bit coming from SW[0]) and the output of the multiplexer is displayed on
LEDR0. This is for labeling purposes only, not because we expect you to upload your design
onto the DE1-SOC board.
(b) How big does the multi-bit input need to be to provide all the inputs to the 7-to-1 multiplexer?
Provide your answer in your report. (PRELAB)
2. Build your circuit in Logisim, using a 7-to-1 multiplexer and the splitter components. Make sure
your implementation reflects your design in the previous step, including the labels. (PRELAB)
3. Simulate your circuit with test vectors in Simulate > Test Vector.... Include a screenshot of the
simulation output as part of your prelab report. (PRELAB)
5 Part II
Figure 1(a) shows a circuit for a full adder, which has the inputs a, b, and ci
, and produces the outputs
s and co. Parts b and c of the figure show a circuit symbol and truth table for the full adder, which
produces the two-bit binary sum cos = a + b + ci
. Please note that the + operator here means addition
and not logic OR. Figure 1(d) shows how four instances of this full adder module can be used to design
a circuit that adds two four-bit numbers. This type of circuit is called a ripple-carry adder, because of
the way that the carry signals are passed from one full adder to the next. Build this circuit in Logisim,
as described below. Be sure to use what you learned about hierarchy in Lab 2.
2
FA
0
1
ci
a) Full adder circuit
a
b co
s ci
a
b co
s
b) Full adder symbol
FA
a0 b0
s0
FA
c1 a1 b1
s1
FA
c2 a2 b2
s2
FA
c3 a3 b3
s3 cout
d) Four-bit ripple-carry adder circuit
cin
0
0
c) Full adder truth table
a ci b
0 0
0 1
0
0
1 0
1 1
1 0 0
1
1
0 1
1 0
1 1 1
0
0
c s o
0
1
0
1
1
0
0 1
1
1
0
0
1 1
Figure 1: A ripple-carry adder circuit.
Perform the following steps:
1. Draw a schematic showing your code structure with all wires, inputs and outputs labeled. Your
schematic should resemble Figure 1(d), though it should also contain module and signal labels, and
shows external connections to switches and LEDs (use SW3-0 for A, SW7-4 for B and SW8 for
Cin. Use LEDR4-0 for the outputs). Be prepared to explain your approach to the TA as part of
your preparation. (PRELAB)
2. Build the module for the full adder subcircuit and build a larger module that instantiates the four
instances of this full adder. Name the input ports A, B and cin, and the output ports S and cout.
Note: You should NOT use Logisim’s built-in arithmetic addition component in your full-adder.
Doing so will earn you 0 marks for this part. (PRELAB)
3. Simulate your 4-bit ripple-carry adder with test vectors for intelligently chosen values of A, B and
cin. You should include a screenshot of it in the prelab. Note that as circuits get more complicated,
you will not be able to simulate or test all possible cases. This means that you can test only a
subset. Here intelligently chosen means to find particular corner cases that exercise key aspects
of the circuit. An example would be a pattern that shows that the carry signals are working. Be
prepared to explain why your test cases are good enough. (PRELAB)
6 Part III
Using Part II from this lab and the HEX decoder from Lab 2 Part III (import your earlier modules from
File > Merge and make sure all the modules have different names), you will implement a simple Arithmetic Logic Unit (ALU). The ALU generally has two data inputs and can perform multiple operations
on these data inputs such as addition, subtraction, logical operations, etc. The operation performed by
the ALU is determined by another multi-bit input (called the function input) that specifies the output
operation for the ALU.
3
The easiest way to build this ALU is to:
1. Create modules that implement all of the required operations and then connect the outputs of
these modules to the inputs of a multiplexer.
2. Choose the operation that appears on the ALU output by using the ALU function inputs (connected
to the multiplexer select lines).
3. Display the unsigned inputs A and B on two seven-segments displays.
4. Display the output of the ALU on eight LEDs (binary value) and two more seven-segment displays.
The following table shows the operations that you should implement in the ALU, given the specified
function value.
function values logic
0 Make the output equal to A+1, using the adder
circuit from Part II of this Lab.
1 A + B using the adder from Part II of this lab
2 A + B using the Adder component found in Arithmetic
3 Bitwise A XOR B in the lower four bits and A OR B in the
upper four bits
4 Output 1 (8’b00000001) if any of the 8 bits in
either A or B are high, and 0 (8’b00000000)
if all the bits are low (also known as a reduction OR operation)
5 Make both inputs appear at the output, with A in
the most significant (left-most) four bits and
B in the least significant (right-most) bits.
Note that the ALU takes in two unsigned 4-bit inputs, A and B and outputs an unsigned 8-bit value
called ALUout[7:0]. Note that in some cases, the output will not require the full 8 bits so you will
need to do something reasonable with the extra bits, such as making them 0 so that the value is still
correct. Adding zeroes in front of any positive number is called sign-extension, and does not change the
value of the number. In Logisim this is achieved by using Wiring > Bit Extender (details can be found
http://www.cburch.com/logisim/docs/2.6.0/en/libs/base/extender.html).
Perform the following steps to complete the lab:
1. Draw a schematic showing your module structure as a block diagram with all wires, inputs and
outputs labeled. Feel free to include multiple schematics if you wish to illustrate multiple levels in
your design hierarchy. In particular, clearly highlight the multiplexer for your ALU as well as all
inputs to this multiplexer. Be prepared to explain your design choices to the TA. (PRELAB)
2. Build the Logisim module for the ALU including all high-level inputs and outputs. (PRELAB)
3. Simulate your circuit with test vectors for a variety of input settings, ensuring the all the tests are
passing. Include screenshots of your successful test output as part of your prelab. (PRELAB)
4. Prepare your design and implementation for your in-lab demo. (PRELAB)
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