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V22.0436 - Prof. Grishman

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Assignment 2: Comparator

0. Read the Logisim documentation about Libraries and Subcircuits
by clicking on "Help>Help Contents". This describes how to
build small devices and save them for future use in building larger
devices. Note that each time you want to create a new subcircuit
that you will use later on, you should click on "Project>Add
Circuit".

1. Build a 1-bit comparator. Using Logisim, construct a
device (from AND, OR, XOR, NOT, NAND, NOR, and XNOR gates) that has two
inputs, a and b, and two outputs, a=b and a>b. Output a=b is a 1 if a and b are the same (both 0 or both
1); output a>b is a 1
if a is greater than b (in other words, a is a 1 and b is a 0).

Be sure to click on "Projects>Add Circuit" before creating the
1-bit comparator. It will ask you for a name for the
circuit. Call it "one bit comparator".

2. Build a 3-bit comparator from 1-bit comparators.
Using Logisim, construct a circuit which has two 3-bit inputs, A = a_{2}a_{1}a_{0}
and B = b_{2}b_{1}b_{0},
and one output, greater.
greater should be 1 if A > B when A and B are interpreted as unsigned binary
integers. The circuit should be built from 3 of your 1-bit
comparators, connected together with AND and OR gates. Save this
as the "main" part of your circuit (double-click on "main" before
entering this circuit).

To see how they should be combined, consider the simpler case of
2-bit inputs, A = a_{1}a_{0}
and B = b_{1}b_{0}.

Then greater should be 1 if a_{1}>b_{1} OR ((a_{1}=b_{1}) AND (a_{0}>b_{0})).

You should use the same approach, but extended to the 3-bit case.

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Due in one week: September 29th.

Mail your homework (the .circ file) to grishman@cs.nyu.edu and mark
the mail CompArch -- Asgn 2.