D - two's complement binary numbers, Two's complement binary numbers, Appendix – Rockwell Automation 1746-NI8 SLC 500 Analog Input Modules User Manual User Manual
Page 82
Appendix
D
Publication 1746Ć6.8 - April 1997
Two's Complement Binary
Numbers
The SLC 500 processor memory stores 16-bit binary numbers.
Two’s complement binary is used when performing mathematical
calculations internal to the processor. Analog input values from the
analog modules are returned to the processor 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
processor 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. As indicated in
the figure below, this limits the maximum positive decimal value to
32767 (all positions are 1 except the far left position). For 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
0
1
1
1 1
1 1
1
1
1 1 1
1
1 1
1x
2
14 =
16384
0
x
2
15 =
0
This position is always zero for positive numbers
1x
2
13 =
8192
1x
2
12 =
4096
1x
2
11 =
2048
1x
2
10 =
1024
1x
2
9 =
512
1x
2
8 =
256
1x
2
7 =
128
1x
2
6 =
64
1x
2
5 =
32
1x
2
4 =
16
1x
2
3 =
8
1x
2
2 =
4
1x
2
1 =
2
1x
2
0 =
1
16384
8192
4096
2048
1024
512
256
128
64
32
16
8
4
2
1
32767