HW #4
CSEE W3827 - Fundamentals of Computer Systems
Spring 2013
Due 2:25pm at the end of class on 2/25/2013
Prof. Rubenstein
Topics: Standard circuitry (encoder, decoder mux), combinatorial circuit design
Note that this homework has 7 problems and is 2 pa

HW #4 Solutions
CSEE W3827 - Fundamentals of Computer Systems
Spring 2013
Topics: Standard circuitry (encoder, decoder mux), combinatorial circuit design
Solutions prepared by David (partially adapted from F10).
Please see TAs Lisa and Andrew for question

Midterm Solutions
CSEE W3827 - Fundamentals of Computer Systems
Fall 2010
Oct. 21, 2010
Prof. Rubenstein
This midterm contains 3 questions, and totals 100 points. To get full credit you must answer all questions. BOOKS
AND NOTES ARE PERMITTED, BUT ELECTRO

HW #2 Solutions
CSEE W3827 - Fundamentals of Computer Systems
Due 2/11/2013
Spring 2013
Prof. Rubenstein
Topics: Basic algebraic manipulation, DeMorgans laws, duals, complements, prod-of-sum, sum-of-prod, NAND
and NOR gates
Note that this homework has 7 p

Sample Midterm Solutions (Fall 2009)
CSEE W3827 - Fundamentals of Computer Systems
Fall 2010
Given Oct. 22, 2009
Prof. Rubenstein
This midterm contains 3 questions, and totals 100 points. To get full credit you must answer all questions. BOOKS
AND NOTES A

HW #1 Solutions
CSEE W3827 - Fundamentals of Computer Systems
Fall 2010
Topics: binary number representations (2-complement, 1-complement, oating point)
Note that this homework has 7 problems and is 2 pages long.
Due 2/4/2013
Prof. Rubenstein
1. (20 pts)

Sample Midterm Solutions
CSEE W3827 - Fundamentals of Computer Systems
Fall 2008 (Midterm originally Given Fall 2007)
Oct. 15, 2007
Prof. Rubenstein
This midterm contains 3 questions, and totals 100 points. To get full credit you must answer all questions

HW #5
CSEE W3827 - Fundamentals of Computer Systems
Spring 2013
Due 2:25pm at the end of class on 3/4/2013
Prof. Rubenstein
Topics: ip-ops, state design, sequential circuit design, ROM and PLAs
Note that this homework has 5 problems and is 1 page long.
1.

CSE E W3827 - F undamentals of Computer Systems
Prof. Rubenstein
M idterm Solution
1. (20 pts.)
a) (3 pts) What is the value of 11010 if it represents a binary number in 2s
complement form?
Solution: 11010 in 2s complement can be converted to decimal as f

HW #5 Solutions
CSEE W3827 - Fundamentals of Computer Systems
Spring 2013
Topics: ip-ops, state design, sequential circuit design, ROM and PLAs
Solutions prepared by Thomas (partially adapted from F10).
Please see TAs David and Nidhi for questions about g

Fundamentals of Computer Systems
Memory
Stephen A. Edwards
Columbia University
Spring 2012
Atari Space Race, 1973
Atari Space Race PCB
Front
Back (mirrored)
Read-Only Memories: Combinational Functions
Ak1
Dn1
.
.
.
.
2k n
.
.
A2
ROM
D1
A1
D0
A0
General RO

Fundamentals of Computer Systems
Finite State Machines
Stephen A. Edwards
Columbia University
Spring 2012
Finite State Machine Components
Current State
Inputs
Next State
C
L
Next State
C
L
Outputs
Current State
CLOCK
Current State
Inputs?
Moore and Mealy

Fundamentals of Computer Systems
Review for the Final
Stephen A. Edwards
Columbia University
Spring 2012
The Final
3 hours
810 problems
Closed book
Simple calculators are OK, but unnecessary
One double-sided 8.5 11 sheet of your own notes
Anything discuss

Fundamentals of Computer Systems
The MIPS Instruction Set
Stephen A. Edwards
and
Martha A. Kim
Columbia University
Spring 2012
Instruction Set
Architectures
MIPS
The GCD Algorithm
MIPS Registers
Types of Instructions
Computational
Load and Store
Jump and

Fundamentals of Computer Systems
Review for the Midterm
Stephen A. Edwards
Columbia University
Spring 2012
The Midterm
75 minutes
45 problems
Closed book
Simple calculators are OK, but unnecessary
One double-sided 8.5 11 sheet of your own notes
Anything d

Fundamentals of Computer Systems
Transistors, Gates, and ICs
Stephen A. Edwards
Columbia University
Spring 2012
Semiconductor
semiconductor
noun
1. a substance, such as silicon or germanium, with
electrical conductivity intermediate between that of an
ins

Fundamentals of Computer Systems
Thinking Digitally
Stephen A. Edwards and Martha Kim
Columbia University
Spring 2012
The Subject of this Class
0
The Subjects of this Class
0
1
But let your communication be, Yea, yea; Nay, nay: for
whatsoever is more than

Fundamentals of Computer Systems
Combinational Logic
Stephen A. Edwards
Columbia University
Spring 2012
Encoders and Decoders
Decoders
Input: n-bit binary number
Output: 1-of-2n one-hot code
2-to-4
in
out
00
01
10
11
0001
0010
0100
1000
Decoders
Input: n-

Fundamentals of Computer Systems
Sequential Logic
Stephen A. Edwards
Columbia University
Spring 2012
State-Holding Elements
Bistable Elements
Q
Q
Q
Q
Equivalent circuits; right is more traditional.
Two stable states:
0
1
1
0
A Bistable in the Wild
This de

Fundamentals of Computer Systems
Bresenhams Line Algorithm in Hardware
Stephen A. Edwards
Columbia University
Spring 2012
Bresenhams Line Algorithm
Objective:Draw a line.
Bresenhams Line Algorithm
.with well-approximating pixels.
Bresenhams Line Algorithm

Fundamentals of Computer Systems
Boolean Logic
Stephen A. Edwards
Columbia University
Spring 2012
Boolean Logic
George Boole
18151864
Booles Intuition Behind Boolean Logic
Variables X, Y, . . . represent classes of things
No imprecision: A thing either is

HW #6 Solutions
CSEE W3827 - Fundamentals of Computer Systems
Spring 2013
Topics: Register design and memory design; coincident selection
Solutions prepared by Nidhi (partially adapted from F10).
Please see TAs Thomas and Andrew for questions about gradin

HW #2
CSEE W3827 - Fundamentals of Computer Systems
Spring 2013
Due 2:25pm at the end of class on 2/13/2013
Prof. Rubenstein
Topics: Basic algebraic manipulation, DeMorgans laws, duals, complements, prod-of-sum, sum-of-prod, NAND
and NOR gates
Note that t

Midterm
CSEE W3827 - Fundamentals of Computer Systems
Fall 2010
Oct. 21, 2010
Prof. Rubenstein
This midterm contains 3 questions, and totals 100 points. To get full credit you must answer all questions. BOOKS
AND NOTES ARE PERMITTED, BUT ELECTRONIC DEVICE

CSEE W3827 Fall08 midterm: p. 1
YOUR NAME:
Midterm
CSEE W3827 - Fundamentals of Computer Systems
Fall 2008
Oct. 20, 2009
Prof. Rubenstein
This midterm contains 4 questions, and totals 100 points. To get full credit you must answer all questions. BOOKS
AND

Sample Midterm (Fall 2009)
CSEE W3827 - Fundamentals of Computer Systems
Fall 2010
Given Oct. 22, 2009
Prof. Rubenstein
This midterm contains 3 questions, and totals 100 points. To get full credit you must answer all questions. BOOKS
AND NOTES ARE PERMITT

Final from Fall07
CSEE W3827 - Fundamentals of Computer Systems
Fall 2007
Dec. 19, 2007
Prof. Rubenstein
This nal contains 4 questions, and totals 100 points. To get full credit you must answer all questions. BOOKS
AND NOTES ARE PERMITTED, BUT ELECTRONIC

Final Exam
CSEE W3827 - Fundamentals of Computer Systems
Fall 2010
Dec. 21, 2010
Prof. Rubenstein
This nal contains 5 questions, each worth 25 points. If you answer all questions, your grade will be the sum of
your 4 best scores. BOOKS AND NOTES ARE PERMI

Final Exam Solutions
CSEE W3827 - Fundamentals of Computer Systems
Fall 2009
Dec. 21, 2010
Prof. Rubenstein
This nal contains 5 questions, each worth 25 points. If you answer all questions, your grade will be the sum of
your 4 best scores. BOOKS AND NOTES