This preview shows pages 1–3. Sign up to view the full content.
1
1
BME 303 Lecture 5
• Briefly Review & Finish: Boolean logic
–HW #1 due today – turn it in now!
–HW #2 due next Tuesday, February 8
–Looking ahead: Exam 1 in 3 weeks
2
Class website: At last!
• I just obtained access to
Blackboard! – will update
everything (consistent between
sections) tonight
3
BME Tutors
• Engineering Study Table: MonThur 7:30
pm – 9:30 pm, Jester City Limits
• For BME 303:
davidrains@mail.utexas.edu
–John Beck: Thur
johnbeck@mail.utexas.edu
–Plus other times by arrangement
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
fraction
(23bit)
exponent
(8bit)
s
Floating Point: “Trees”
• Representation:
N = (
1
)
s
·1.
fraction
·2
(exponent127)
(1
exponent
254)
– We “normalize” mantissa by dropping leading 1,
recording only its fractional part
– To handle both positive and negative exponents,
add 127 to the actual exponent to create a “biased
exponent”.
Special cases!
E
x
p
o
n
e
t
=
0
,
(

1
)
S
·
.
f
r
a
c
i
2
6
–
“
d
m
l
z
”
5
I
io
:
+
∞
t =
, fr
tio
±
·2
1
²
N
A
u
b
5
Floating Point: “Forest”
• We need to store somehow, no “natural”
format (like 2’s complement for integers),
so some arbitrary choices were made
• Arithmetic with floating point is complex to
implement
• Special cases: Overflow (±
∞
), Underflow
(±0), Illegal results (NAN)
• Floating point
calculations
posses these
problems – format just reflects that –
numerical methods is an entire discipline
6
Operations: Arithmetic and Logical
•
A data type includes
representation
and
operations
.
• We’ve seen representation for signed
integers, and these arithmetic operations:
– Addition
– Negation
– Subtraction
– Sign Extension
– Shift left (x by 2)
– Shift right (÷ by 2)
• Arbitrary multiplication, division, etc., can
be built from these basic operations.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document2
7
Another use for bits: Logic
• Beyond numbers
– Logical variables: true or false, on or off, etc.
–readily represented by binary
– Logical variable A can take the values false
= 0 or true = 1 only.
– The manipulation of logical variables is
known as Boolean Algebra – has its own set
of operations not to be confused with
arithmetical operations
– Some basic operations: NOT, AND, OR
8
AND Operation
• AND
is a binary logical operation, i.e., as
defined earlier, it has two operands.
• Letting A and B denote
the operands, A
AND
B = 1
if and only if both
A = 1 and
B = 1
• 1 AND B = ?, 0 AND B = ?
A
This is the end of the preview. Sign up
to
access the rest of the document.
 Spring '08
 Ren

Click to edit the document details