Fall-09 18-240 L8 —
Finite Number Representation
!
What?
"
Counting, base conversion, positional systems, signed
numbers, arithmetic, etc.
!
Why?
"
Isn’t this like learning the multiplication tables in 3rd grade?
"
Actually more like how to count and add in 1
st
grade.
But you
need some basic building blocks …
!
Where?
"
As in, where is this useful?
"
Everywhere: Digital computers are all about and based on
numbers! High performance arithmetic, supercomputers,
signal processing, etc.
"
And . . .
3
!
What do you need to “represent” a number?
"
Need a base or radix =
r
"
Need
r
unique symbols (digits in base 10)
"
r = 10
digits = {0,1,2,3,4,5,6,7,8,9}
"
r = 2
digits = {0,1}
"
r = 8
digits = {0,1,2,3,4,5,6,7}
"
r = 16
digits = {0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F}
!
Number Structure
"
Place value for digit d
i
is
"
Value of a number is
So far this is very natural and unambiguous for positive numbers.
Don't confuse what is a number with how to represent it.
Fall-09 18-240 L8 —
Non-Decimal Representations
… d
2
d
1
d
0
. d
-1
d
-2
…
radix
point
4