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EC262 Topic 8: The Design of Iterative Systems
Iterative Systems
Most of you (I would guess
all
of you) have computers with microprocessors that support the socalled
x8664
instruction set. This means, among other things, that your computer is able to add together two 64bit quantities.
Let’s consider this problem: You are back in the year 1999, leading the AMD team that is tasked with building
a circuit to add two 64bit binary numbers together.
One of your team members vaguely remembers his EC262
class, and announces that such a circuit can be built with a combinational logic circuit.
He proposes a system
with no modularity—a system that directly inputs the two 64bit binary numbers to be added (and a carryin bit)
and directly outputs the 64bit sum (with a possible 65
th
carry out bit).
He shows you a schematic that looks
like a huge vat of spaghetti accidentally spilled on the floor of King Hall (before it is picked up by the cleaning
crew and served to hungry midshipmen).
You ask your team member:
How many lines are in your truth table?
What is his reply?
The number of lines in a truth table is:
If a supercomputer could process 1 billion lines of this truth table every second, how long would it take to
examine the truth table?
Your team member tells you he tried to implement his circuit on a protoboard, but the sheer number of wires
caused flame and smoke.
You fire the team member (just as he is offering to show you his 129variable
Karnough map) because you remember from EC262 that there is a better way to do this:
Note that this is precisely how you perform addition!
You start at the least significant digit, and, digitbydigit,
calculate the sum and carry.
Your design can be described by a truth table with ____
lines and with
Systems that are built by combining a number of identical blocks are termed
The Delay Problem
Look at the above picture.
Suppose all of the bits in the two numbers to be added—i.e.,
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 Spring '08
 NASIS
 Microprocessor, Delay, Least significant bit, Alan Marcovitz, 64bit adder, Iterative Systems

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