Appendix A
Understanding Binary and Hexadecimal
Numbering Systems
The Binary System:
A Short Primer
To best understand some of the references in the
CP-220
Central Station Receiver Hook-Up and Installation Manual,
a
brief look at the Binary System and the Hexadecimal System,
which follows, is recommended.
The Binary System is simply another way of identifying
numbers, but unlike the Decimal System, it uses only two
digits: "0" and "1," called
binary digits
or
bits
. Employing only
two numbers (instead of ten) makes the Binary System ideal
for use with digital circuitry, which responds to just two
electrical states and is used extensively in the CP-220 Central
Station Receiver. One could say that the Binary System is the
language
of digital electronics.
DECIMAL
BINARY
DIGIT POSITION:
4th
3rd
2nd
1st
"BIT" POSITION:
4th
3rd
2nd
1st
PLACE VALUE:
1000
100
10
1
PLACE VALUE:
8
4
2
1
DERIVED FROM:
10
3
10
2
10
1
10
0
DERIVED FROM:
2
3
2
2
2
1
2
0
Examples:
23
10
=
(2x10
1
) + (3x10
0
)
149
10
= (1x10
2
) + (4x10
1
) + (9x10
0
)
9052
10
= (9x10
3
) + (0x10
2
) + (5x10
1
) + (2x10
1
)
Examples:
10
2
=
(1x2
1
) + (0x2
0
)
101
2
= (1x2
2
) + (0x2
1
) + (1x2
0
)
1101
2
= (1x2
3
) + (1x2
2
) + (0x2
1
) + (1x2
0
)
TABLE A-1
The Binary System is structured in a manner similar to the
Decimal System, in which the value of any bit is determined
by its position in the number. Table A-1 compares how the
Decimal and Binary Systems handle numbers.
Note that the value of any digit or bit position is derived by raising
the
base
of the respective number system (either "10" [decimal] or
"2" [binary]) to an additional
power
for each subsequent digit (or
bit) after the rightmost column. Numbers in this position (called
the
least significant digit (or bit)
are always worth "1" times the
number's value.
Page A-1
Appendix A: Understanding Binary
CP-220A Central Station Receiver
and Hexadecimal Numbering Systems Hook-Up and Installation Manual