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Workshop 2
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- Computer Architecture
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- University Of Lincoln (UoL)
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Lincoln School of Computer ScienceUniversity of Lincoln
CMP1125MComputer Architectures
Digital Logic
1 Introduction
The goal of this workshop is to exercise some of the concepts behind Digital Logic. Please refer to
the previous workshop description document for further details about the workshop organisation
and how to get help.
This workshop includes an introductory tutorial teaching you how to use a logic simulator and a set
of tasks which will help you to understand concepts covered during lectures. If it happens that your
workshop session precedes the lecture, refer to lecture slides and additional material provided with
the tasks. The tasks involve practical applications of Boolean algebra and therefore your notes from
the Maths module might be very handy. As usual, ** indicates more difficult questions.
2 Bool Arithmetic
Simplifying the following Boolean expressions, based on theorems in lecture slides 8 and 9:
i 𝐴 + 𝐴𝐵 ii 𝐴𝐵 + 𝐴𝐵̅ iii 𝐴𝐵 + 𝐴(𝐶𝐷 + 𝐶𝐷 ̅ ) v ̅̅̅̅̅̅̅̅̅̅̅̅
̅ ) iv (𝐵𝐶̅ + 𝐴̅𝐷)(𝐴𝐵̅ + 𝐶𝐷 𝐴(𝐴 + 𝐶)
̅̅̅̅̅̅̅̅̅
vi 𝐴 + 𝐵𝐶̅̅̅̅ vii 𝐴̅𝐵𝐶 + 𝐴𝐶 viii 𝐴(𝐵 + 𝐴)(𝐶 + 𝐵)𝐵̅ ix 𝐴𝐵 + 𝐵𝐶̅ + 𝐴𝐶 x 𝐴(𝐵 + 𝐴(𝐵 + 𝐶𝐵̅))
3 LogicSim – Tutorial
We are going to use LogicSim to design, simulate and test digital logic circuits. It is a Java program
written by Andreas Tetzl. The program and related information can be obtained from the following
website www.tetzl.de. Download a standalone version of the program (from http://www.tetzl.de/
java_logic_simulator.html#download or Blackboard), extract all files and double click on the
LogicSim.jar file to run the program.
To run LogicSim.jar you need to firstly install JAVA. At least version 1.4 of the JAVA Runtime
Environment is needed and can be downloaded from http://www.java.com/ . To start LogicSim,
extract the archive content and double click on LogicSim.jar or run "java -jar LogicSim.jar" (under
the directory where LogicSim.jar is, in Command Prompt)
Create a new project (menu File/New) and explore the program a little. Make sure that the
Settings/Gate Design option is set to the US/ISO standard; otherwise you will see the alternative
gate symbols. Select circuits from the list on the left side and place them on the work panel. To
connect two circuits, click the output of one circuit (on its right side) and draw a wire to an input of
another circuit. You can also connect a new wire to the existing ones by holding down the shift key
and clicking at the same time the desired point on the existing wire. Circuits and wires can be
activated by clicking on them and then deleted with the DEL key. The ESC key allows you to delete
the last segment of the wire.
, When the simulation button is pressed, the simulation runs. It is possible to edit circuits while the
simulation is running but this is not recommended, as it might make everything to run slow – so
remember to stop the simulation before changing your design. The colour of wires indicates the
signal value: black = 0 and red = 1.
3.1 Simple Circuit
Using two LEDs and two switches to build the above circuit. Run the simulation, and check that it
works as expected. Note that some devices have properties that can be accessed by right clicking
on the device. Explore the properties for switches and see what happens when you change
them.
3.2 Logic Gates
Construct and simulate the following circuit with an AND gate. (You can label the inputs and outputs
with the “Text Label” component).
X Y Z
0 0 0
0 1 0
1 0 0
1 1 1
On the right side there is a truth table for the AND gate listing all possible combinations of input and
output values. Check if the behaviour of your circuit corresponds to the values in the truth table.
4 Combinatorial Circuits
• The NAND gate is a universal gate – i.e. it can be used to construct other gates and circuits.
Build and test one of the following circuits: OR, XOR or NOR using the NAND gates only.
Check the following article for inspiration: https://en.wikipedia.org/wiki/NAND_logic.
• Construct a truth table for the following Boolean function: w = x (y z + x y). The
Boolean operators involved include Boolean product (·), sum (+) and inverse (indicated by an
overbar). You may want to refer to your Maths notes on Logic if you do not know how to
proceed.
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