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15-251: GTI
Guide to Drawing Circuits
February 18, 2003
The purpose of this document is to introduce you to the mechanics of drawing circuit
diagrams. This should help you make your diagrams neat and clear, and thus understandable.
This is necessary for you to think about and verify your design, and for us to grade it.
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Gates
Basic gates are drawn like this:
AND
OR
NOT
XOR
The two wires going into the left side of each gate are the inputs, the wire coming out of
the right is the output. Gates and simple circuits are conventionally drawn facing to the right
like this, but in more complex circuit diagrams they can be drawn facing in any direction; the
shape of the circuit will indicate the direction of signal ow along the wire. (The signal is
the boolean value on the wiretrue or false, 1 or 0.)
Note that the only major dierence between AND and OR is the shape of the back. Thus
be sure to always make the backs of your ORs concave and the backs of your ANDs at.
That little circle on the nose of the NOT gate is called a bubble, and in general it means
that the signal on the wire is negated. Thus by adding a bubble to the front of the AND and
OR gates, we obtain their opposites:
NAND
NOR
1 Dont use just a bubble on a wire to negate a value, though; its much clearer to use a
NOT gate.
Gates are combined by connecting the output of one gate into the input of another:
This (unlabelled) output of this circuit is (x OR y) AND z. Heres a larger circuit:
The output, C, is ((NOT A) AND B) OR (A AND (NOT B)). Note how the inputs A
and B were used multiple times.
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Signal ow
The signal in a circuit ows along the wires, and through each gate from its input to its
output. This means that a gate is constantly looking at its inputs, computing the appropriate
value, and putting that value on its output. We say that the gate drives its output.
If you wish to use the output of a gate as an input multiple times, you may split the wire:
2 This circuit computes two values: (A OR (NOT B)), and ((NOT B) OR C).
Be careful, though: Each wire must be driven by exactly one gate. You cant have an
input that comes from nowhere, or a wire which is connected to the output of two gates.
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Thus, the following circuits are illegal:
You must also be careful about loops in your circuits. You can feed the output of a circuit
back into a prior spot in the circuit, but it must be done properly. Specically, there must
be a clocked gate in any loop. The clock will stop the signal from zipping around the loop as
fast as it can. So the following is bad:
(What would happen in such a circuit?) But this is OK:
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If you do these things in real physical hardware, nasty things happen, like short circuits.
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Wires
As youve probably noticed, wires are conventially drawn as always travelling either horizon-
tally or vertically. This just helps to make the diagrams neater.
When your circuits get complex and involve many gates, you will inevitably need to have
two unconnected wires cross on your diagram. To avoid confusion, draw one of the wires
jumping over the other:
Also, while designing your processor, you will want to deal with inputs to circuits which
are multiple bits, which means multiple wires. A 32-bit number in a computer is carried on
32 separate wires. This is drawn as a bundle:
Joining and splitting wires is denoted thus:
4 In the second gure, a bundle of 4 bits is split into two single bits (bits 0 and 3 of the
bundle), and a bundle of 2 (consisting of bits 1 and 2).
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Modules
A key technique in building the processor (or any complex engineering design) is modularity.
Once you have designed a circuit with a specic purpose and function, you may make that
circuit into a module with certain inputs and outputs. From that point on, you need only
draw the module as a labelled box, rather than drawing the entire circuit again each time.
This will save you eort and paper, but more importantly it will clear away mental clutter
and make the diagram easier to comprehend.
Suppose you wanted to make a module out of the rst circuit we saw above:
You would draw a box around it and give it a name (as well as naming all its inputs and
outputs):
5 From then on you would draw it as follows:
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You would put it in circuits just like a basic gate.
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Software options
You can draw circuits in Microsoft Word or use an X Windows drawing program called xfig.
Check out the course webpage at http://www.discretemath.com for information on drawing
circuits in these programs. There are some software packages designed specically for drawing
circuit diagrams (Visio for Windows is great), but we dont know of any available in the cluster
and cannot oer documentation for those packages.
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