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8-13. Terminology
In general, programmable controllers work with binary numbers in one form
or another to represent various codes or quantities. The binary number
system uses the number 2 as the base and the only allowable symbols are “0”
and “1”. There are no 2s, 3s, etc. Each digit of binary is called as “bit”. “Bit”
means “binary digit”. A group of 8 bits is called a “byte” and a group of 16
bits (two bytes) is called a “word”.
The binary number “0000000000101011” is expressed in decimal as follows:
1
×
2
0
+ 1
×
2
1
+ 0
×
2
2
+ 1
×
2
3
+ 0
×
2
4
+ 1
×
2
5
+ ..... + 0
×
2
15
= 1 + 2 + 0 + 8 + 0 + 32 + ..... + 0
= 43
One of the codes expressed in binary. BCD is a binary code in which each
decimal digit from 0 to 9 is represented by four binary digits (bits). The four
positions have a weighted value of 1, 2, 4, and 8, respectively, starting with
the least significant bit. A thumbwheel switch is specified as a BCD device,
and when connected to a programmable controller, each decimal digit
requires four inputs.
BCD is usually expressed grouping four bits as one digit in the same way as
the hexadecimal constant H. When BCD is grouped in four bit units, the
BCD is expressed by adding the prefix H to the data. Since the weight of
each BCD H code is same as that of decimals, be sure to pay attention
not to be confused with hexadecimal numbers when BCD H code is
handled.
Example: When K1993 (decimal) is expressed in BCD.
BCD code
0 0 0 1 1 0 0 1 1 0 0 1
0 0 1 1
Decimal 1 9 9 3 K
BCD H code 1 9 9 3 H
10 0
×
3 = 3
10 1
×
9 = 90
10 2
×
9 = 900
10
3
×
1 = 1000
0 0
11
0
8
0 1 1 1
3 0
0
15
0
14 13
0
12
0
10
0
9
0
2 1
0
7 4
0
6
1
5 Bit position
Binary data
Most significant bit
(MSB) Least significant bit
(LSB)
byte byte
word
binary:
Binary Coded Decimal (BCD):