V-Memory; Binary-Coded Decimal Numbers; Hexadecimal Numbers - Automationdirect.com DirectLOGIC DL205 Series User Manual

Chapter 3: CPU Specifications and Operations
V–Memory
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Variable memory (called "V-memory") stores data for the ladder program and for configuration settings.
V-memory locations and V-memory addresses are the same thing, and are numbered in octal. For
example, V2073 is a valid location, while V1983 is not valid ("9" and "8" are not valid octal digits).
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Each V-memory location is one data word wide, meaning 16 bits. For configuration registers, our manuals will
show each bit of a V-memory word. The least significant bit (LSB) will be on the right, and the most significant bit
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(MSB) on the left. We use the word "significant," referring to the relative binary weighting of the bits.
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V-memory data is 16-bit binary, but we rarely program the data registers one bit at a time. We use
instructions or viewing tools that let us work with binary, decimal, octal, and hexadecimal numbers. All
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these are converted and stored as binary for us. A frequently-asked question is "How do I tell if a number is
binary, octal, BCD, or hex"? The answer is that we usually cannot tell by looking at the data, but it does not
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really matter. What matters is: the source or mechanism which writes data into a V-memory location and
the thing which later reads it must both use the same data type (i.e., octal, hex, binary, or whatever). The V-
memory location is a storage box... that's all. It does not convert or move the data on its own.
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Binary-Coded Decimal Numbers

Since humans naturally count in decimal, we prefer to enter and view PLC data in decimal as well (via
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operator interfaces). However, computers are more efficient in using pure binary numbers. A compromise
solution between the two is Binary-Coded Decimal (BCD) representation. A BCD digit ranges from 0 to
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9, and is stored as four binary bits (a nibble). This permits each V-memory location to store four BCD
digits, with a range of decimal numbers from 0000 to 9999.
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In a pure binary sense, a 16-bit word represents numbers from 0 to 65535. In storing BCD numbers, the
range is reduced to 0 to 9999. Many math instructions use BCD data, and DirectSOFT and the handheld
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programmer allow us to enter and view data in BCD. Special RLL instructions convert from BCD to
binary, or visa–versa.
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Hexadecimal Numbers

Hexadecimal numbers are similar to BCD numbers, except they utilize all possible binary values in each 4-
A
bit digit. They are base-16 numbers so we need 16 different digits. To extend our decimal digits 0 through
9, we use A through F as shown.
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A 4-digit hexadecimal number can represent all 65536 values in a V-memory word. The range is from
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0000 to FFFF (hex). PLCs often need this full range for sensor data, etc. Hexadecimal is a convenient way
for humans to view full binary data.
D
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DL205 User Manual, 4th Edition, Rev. B
V-memory address
(octal)
V2017
BCD number
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0 1 0 0
V-memory storage
Decimal 0 1 2 3
Hexadecimal 0 1 2 3
Hexadecimal number
1 0 1 0
V-memory storage
V-memory data
(binary)
MSB
0 1 0 0 1 1 1 0 0 0 1 0 1 0 0 1
4 9
4 2 1 8 4 2 1
1 0 0 1
4 5 6 7 8 9 10 11 12 13 14 15
4 5 6 7 8 9
A 7
0 1 1 1
LSB
3 6
8 4 2 1 8 4 2 1
0 0 1 1 0 1 1 0
A B C D E F
F 4
1 1 1 1 0 1 0 0