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Appendix A
Understanding Binary and Hexadecimal
Numbering Systems
The Binary System:
A Short Primer
DECIMAL
DIGIT POSITION:
PLACE VALUE:
1000
DERIVED FROM:
Examples:
23
=
(2x10
10
149
=
(1x10
10
9052
=
(9x10
10
Page A-1
Appendix A: Understanding Binary
and Hexadecimal Numbering Systems Hook-Up and Installation Manual
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.
4th
3rd
2nd
100
10
3
2
1
10
10
10
1
0
) + (3x10
)
2
1
0
) + (4x10
) + (9x10
)
3
2
1
) + (0x10
) + (5x10
) + (2x10
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.
1st
"BIT" POSITION:
1
PLACE VALUE:
0
10
DERIVED FROM:
Examples:
10
=
2
101
=
2
1
)
1101
=
2
TABLE A-1
CP-220A Central Station Receiver
BINARY
4th
3rd
2nd
8
4
2
3
2
1
2
2
2
1
0
(1x2
) + (0x2
)
2
1
0
(1x2
) + (0x2
) + (1x2
)
3
2
1
(1x2
) + (1x2
) + (0x2
) + (1x2
1st
1
0
2
0
)
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