Appendix A Base Code Theory; Base 10 (Decimal; Base Code Theory - Pitney Bowes FastPac DI900 Manuallines

Appendix A • Base Code Theory
Base Code
Theory
✍
TIP: The examples in
this appendix represent
only a few of the many
number bases avail-
able and were chosen
because they are
commonly used in the
scanning industry and
on the DI900/DI950.
✍
TIP: Base 10 (decimal)
is the normal number-
ing system we use
daily. It is the number-
ing system we convert
all other numbers to
so we have a standard
frame of reference
when trying to under-
stand numbers ex-
pressed in other bases.
✍
TIP: Each character
position represents a
power of the base. As
an example, for base
10, two characters
allow counting up to
100 number posi-
tions, or 10 to the 2nd
power (10x10 = 100).
A-2
This appendix explains base code numbering theory by showing examples of
different number bases and how it affects counting within the base. Also dis-
cussed is how to convert a number in a base code that is different from our
standard base 10 (decimal) numbering system.
Base 10 (Standard Decimal Number System)
In our decimal number system (Base 10), the rightmost position represents
the "ones" column, the next position represents the "tens" column, the next
position represents "hundreds", etc. Therefore, the number 123 represents 1
hundred and 2 tens and 3 ones, whereas the number 321 represents 3 hun-
dreds and 2 tens and 1 one.
The values of each position correspond to powers of the base of the number
system. So for our decimal number system (base 10), the place values corre-
spond to powers of 10:
... 10,000 1000 100
...10^4 10^3 10^2
Base 10 (Decimal) Number System
4rth (byte)
Character
10x10x10x10
(10 to 4rth
power)
1000's
ASCII
Character->
Maximum
Count Value
(Maximum
Number
Positions)
10
10^1
3rd (byte) 2nd (byte)
Character Character
10x10x10 10 x10
(10 to 3rd (10 to 2nd
power) power)
100's
0 0
1 1
2 2
3 3
4 4
5 5
6 6
7 7
8 8
9 9
0-999
(1,000)
0-9,999
(10,000)
1st (byte)
Character
10
(10 to 1st
power)
10's 1's
0 0
1 1
2 2
3 3
4 4
5 5
6 6
7 7
8 8
9 9
0-9
(10)
0-99
(100)
SV61314 Rev. A