The following terms will be used
in other parts of this manual:
•
most significant bit:
the leftmost bit in a binary
number; the bit position
having the greatest value
•
least significant bit:
the rightmost bit in a binary
number; the bit position having
the least value
In Table A-1,
the least significant digit
is the base of the
number system raised to the
power of zero.
Note that
any
number, when raised to the power of zero, is
always
equal to
"1." Thus, numbers in the columns labeled 2
0
and 10
0
are
simply worth their own value.
Numbers in succeeding columns are each worth more by a factor
equal to the base of the system; the examples at the bottom of
the table illustrate this. To avoid confusion in these examples
and in those that follow, the base of the number system being
represented will be designated by a
10
or a
2
.
The Binary System and Hexadecimal
It should be no surprise that binary numbers will use more
space than their decimal equivalents. A simple number like 9
10
is equal to 1001
2
; 94
10
is equal to 1011110
2
. While the system's
radio equipment handles long streams of binary numbers,
viewing them on the Central Station's terminal would simply be
too much to manage. A technique was needed to abbreviate this
binary data and make it more compact and readable. The
Hexadecimal
numbering system filled the bill perfectly.
Virtually all displays of system data on the terminal will use
hexadecimal to abbreviate the actual binary data.
The Hexadecimal
System
Hexadecimal Numeration
Hexadecimal Numeration (often called
hex
) is based on a
system that uses 16 different characters in its counting
scheme. Unlike the Binary System (which uses "0" and "1") and
the Decimal System (which uses "0" through "9"), the
Hexadecimal System uses both numbers (0 through 9)
and
letters (A through F) to designate its numerals. Hex and
Binary go very well together; we'll soon see that one hex
character can be used to represent four binary bits.
NOTE: To avoid any confusion, when it is necessary to
distinguish hex numbers from other numbers, they will
be identified with a suffix of either "
16
", "H," or "h."
Thus 100
16
, 100H, and 100h all have the same meaning.
Counting in Hex
Tables A-2 and A-3 both show how the Decimal, Binary, and
Hexadecimal systems count from 0 to 15.
CP-220A Central Station Receiver Appendix A: Understanding Binary
Page A-2
Hook-Up and Installation Manual
and Hexadecimal Numbering Systems
