Publication 1769-UM020A-EN-P - December 2009 65
Appendix
D
Two’s Complement Binary Numbers
The controller memory stores 16-bit binary numbers. Two’s
complement binary is used when performing mathematical
calculations internal to the controller. Analog input values from the
analog modules are returned to the controller in 16-bit two’s
complement binary format. For positive numbers, the binary notation
and two’s complement binary notation are identical.
As indicated in the figure on the next page, each position in the
number has a decimal value, beginning at the right with 2
0
and ending
at the left with 2
15
. Each position can be 0 or 1 in the controller
memory. A 0 indicates a value of 0; a 1 indicates the decimal value of
the position. The equivalent decimal value of the binary number is the
sum of the position values.
Positive Decimal Values
The far left position is always 0 for positive values. This limits the
maximum positive decimal value to 32,767 (all positions are 1 except
the far left position).
Positive Decimal Values
EXAMPLE
0000 1001 0000 1110 = 2
11+
2
8+
2
3+
2
2+
2
1
=
2048+256+8+4+2 = 2318
0010 0011 0010 1000 = 2
13+
2
9+
2
8+
2
5+
2
3
=
8192+512+256+32+8 = 9000
1 x 2 = 2
1 x 2 = 1
1 x 2 = 16384
1 x 2 = 8192
1 x 2 = 4096
1 x 2 = 2048
1 x 2 = 1024
1 x 2 = 128
1 x 2 = 512
1 x 2 = 256
1 x 2 = 64
1 x 2 = 32
1 x 2 = 16
1 x 2 = 8
1 x 2 = 4
0 x 2 = 0
0111111111111111
14
13
12
11
10
9
8
7
6
5
4
3
2
1
15
0
16384
8192
4096
2048
1024
512
256
128
64
32
16
8
4
2
1
32767
This position is always 0 for positive numbers.
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