Rockwell Automation 1769-OF4VI Compact I/O Isolated Analog Modules - Manual (Page 117)

1 Publication 1769-UM014B-EN-P - May 2010
Appendix
E
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 32767 (all positions are 1 except the far left position).
Figure E.1 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
0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
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.