Rockwell Automation 1772-L8_LW_LWP_LX_LXP,D17726.5.8 User Manual User Manual
Page 418
Number Systems
Appendix C
C-5
Binary Coded Octal System
The binary coded octal (BCO) format expresses an octal value as an
arrangement of binary digits (eight bits or one byte). The 8 bits are broken
down into three groups: 2 bits, 3 bits, and 3 bits. The first group of binary
digits is used to represent an octal number from 0 to 3; the other two
groups represent an octal number from 0 to 7. All BCO numbers are
composed of these digits.
Each place value in a BCO number represents a power of two starting with
two raised to the zero power (2
0
=1) (Figure C.5). You can compute the
octal number for each group of bits by multiplying the binary digit by its
corresponding place value and adding these numbers together.
Figure C.5
Binary Coded Octal
1
1
1
1
1
1
1
0
2
1
2
1
2
1
2
0
2
0
2
0
2
2
2
2
3 5
7
8
10408ĆI
Get and Put word values use the hexadecimal numbering system. This is a
numbering system made up of 16 digits: the number 0-9 and the A-F. The
letter A-F represent the decimal numbers 10-15, respectively. Four binary
digits represent each hexadecimal character, you can convert from
hexadecimal to binary by writing out the patterns for each hexadecimal
character or group of four binary digits (Figure C.6).
Each place value in a hexadecimal character represents a power of 16
starting with 16 raised to the zero power (16
0
=1) (Figure C.6). You can
compute a decimal number for each group of hexadecimal characters by
multiplying the decimal digit equivalent of each hexadecimal character by
its corresponding place value and adding these number together.
Hexadecimal Numbering
System