Beijing Dublin International College EEEN2003J Digital Electronics
Ripple adder investigation
Equipment: Pen and paper! PC with “logisim” installed Submission
This lab will be marked as one of your graded laboratories. It will be worth 15% of your final grade.
Submit your Logisim project files for half adder, full adder, ripple adder and ripple adder/subtractor as a .zip file to brightspace.
Introduction
The purpose of this laboratory is to further gain experience designing combinatorial logic circuits. You will firstly design a 1 bit half adder and then, using this half adder as a building block, create a 1 bit full adder. Then 4 of these full adders will be combined together to create a 4 bit ripple adder in Logisim.
In the second part of this Lab, you will again use Logisim to investigate how feedback in a digital circuit makes the circuit implicitly time-dependent. You will observe the inner workings of various latches, and you will experiment with the all-important Edge-triggered D-flipflop.
You are required to design and test this circuit.
Tip: Logisim support the concept of having several circuits within the one project file. Doing this allows you to re-use circuits in more complicated designs. Reusing one circuit design multiple times in a larger more complicated circuit. You can create these from the menu item Project->Add Circuit:
If you correctly label the inputs and outputs from each circuit, they can be re-used (several times with one design) as “sub-circuits” in a larger circuits, e.g. the half adder can be used to create a full adder which in turn can be used to create a multi-bit ripple adder. You can also use this technique to create latches which in turn can be modified to become flip-flops.
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Half adder
A 1-bit half adder has two 1-bit inputs, X and Y, and two outputs, Sum (S) and a Carry (C) bit , the truth table is:
00 00 01 01 10 01 11 10
You need to design a circuit to implement the above truth table.
You should implement this in logisim, and test it for all possible input combinations.
1-bit Full adder
A 1-bit full adder is similar to a half adder but it allows also a Carry in bit (Cin), the truth table is as follows:
000 011 101 110 001 010 100 111
This can be designed using the Karnaugh map technique leading to an efficient two level logic implementation, however it can be implemented more efficiently (i.e. using less gates) using multi-level logic. In particular the following circuit, built from two half adders, is very efficient:
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You should implement a 1-bit full adder, using either the karnaugh map technique, or, by using the above circuit – either will work!
Verify the operation of you circuit for all possible combinations of inputs.
4-bit ripple adder
From your lecture notes you should be aware that a 4-bit adder can be made by concatenating x x 1-bit full adders as follows:
You should implement a 4-bit adder, using the above circuit.
Verify the operation of you circuit for a selection of input values (there are 512 possible input combinations, so exhaustive testing is nearly impossible in logisim)
Tip: you can create multi-bit inputs and outputs in logisim and use the “splitter” to obtain the individual bits from the inputs, or to combine bit together into a multi-bit output.
Design and implement an adder/subtractor circuit based on the 4 bit ripple adder with minimal additional logic.
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Ripple adder/subtractor implemented Ripple adder implemented
Full adder implemented
Half adder implemented
circuit re-use, input use, splitter use in logisim