CS 300 – Lecture 3
Intro to Computer Architecture
/ Assembly Language
Digital Design II
Free Food!
Today: Presidents BBQ
1 week: Math dept (Keck's place)
2 weeks: CIS dept (My place)
I encourage all of you to come!
Homework 2
It's in the wiki
Homework 1
Due tomorrow. Morning.
I need details! One line answers probably
won't cut it. A little analysis is important.
Essential Skills
* Rewriting of boolean equations using
Boolean Algebra
* Creating SOP equations
* Conversion between truth tables,
equations, and circuits
Circuit Minimization
One of the big ideas in circuit design is the use of
boolean algebra to rewrite equations to ones that
use fewer gates or have less delay.
The main minimization equation is
AB + AB' = A(B+B') = A
Let's construct a truth table for a "Full Adder" and
then minimize the "Carry".
We won't learn how to minimize in a systematic
way – computers can do this better than you!
Universality
Turing described a "universal machine" – a
computer that is as simple as possible and
yet can do anything that more complex
computers can.
In digital logic, there is a similar idea: a
universal gate. This can be used to
construct ANY machine – no other gates are
needed.
A Universal Logic Gate
Nand:
X
0
0
1
1
Y Output ( 1 = True, 0 = False)
0
1
1
1
How do we make And,
Or, and Not from this?
0
1
1
0
SOP and Hardware
Using NAND is particularly useful when a circuit is
in SOP form. What does SOP look like using only
NAND gates?
We'll stick with AND/OR but the actual circuits are
generally with NAND only.
A PLA is a device that implements large SOP
circuits in a very compact manner
A ROM is a direct encoding of a truth table
Binary Numbers
Everyone here should already know their
Base-2 numbers. If you can't do 4 bit
numbers fast you're not a true CS major!
0010
4
1010
15
1110
6
0111
11
1100
1
Bigger Structures (Design Patterns)
There are a number of common structures that
occur in combinatory circuits.
Multiplexer: (MUX)
Select from a number of different inputs: lots of
inputs, a control, and an output that matches one
input
Demultiplexer (DeMux):
This is the opposite of a MUX – send a single
input to a bunch of different places depending on a
control. Send "0" when the output is not selected.
A 4-1 MUX
A
B
C
D
MUX
Select
Output
A Shifter
Let's design a 1 bit shifter using a MUX.
When the control is 0, we get the data
unaltered. When control is 1, we get left
shifted data.
We'll design this with a 16 bit input – our
"word" size.
How do you convert a 1 bit MUX to a 16 bit
MUX? Does this go slower than the 1 bit
MUX?
Algorithm Design
Hardware algorithms are similar to software
ones but we judge them differently:
* Number of gates
* Overall delay
There are algorithms for all sorts of numeric
operations.
Divide and Conquer
D&C is a classic schema for algorithm
design. Why? Let's look at the design of an
important and common circuit: a barrel
shifter.
Input: 16 bits
Shift Count
How many bits?
Shifted Output (16 bits)
Shifter