Automating Manufacturing Systems - Process Control and ...

plc numbers - 13.10
13.2.2 Other Base Number Systems
Other number bases are typically converted to and from binary for storage and
mathematical operations. Hexadecimal numbers are popular for representing binary values
because they are quite compact compared to binary. (Note: large binary numbers with
a long string of 1s and 0s are next to impossible to read.) Octal numbers are also popular
for inputs and outputs because they work in counts of eight; inputs and outputs are in
counts of eight.
An example of conversion to, and from, hexadecimal is shown in Figure 13.14 and
Figure 13.15. Note that both of these conversions are identical to the methods used for
binary numbers, and the same techniques extend to octal numbers also.
16 3 = 4096
16 2 = 256
16 1 = 16
16 0 = 1
f 8 a 3
15(16 3 ) =
8(16 2 ) =
10(16 1 ) =
3(16 0 ) =
61440
2048
160
3
63651
Figure 13.14
Conversion of a Hexadecimal Number to a Decimal Number
5724
----------- = 357.75
16(0.75) = 12 ’c’
16
357
-------- = 22.3125
16(0.3125) = 5
16
22
----- = 1.375
16(0.375) = 6
16
-----
1
= 0.0625
16(0.0625) = 1
16
1 6 5 c
Figure 13.15
Conversion from Decimal to Hexadecimal
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