Rockwell Automation 1769-IR6 Compact I/O 1769-IR6 RTD/Resistance Input Module - Manual (Page 109)

Rockwell Automation Publication 1769-UM005B-EN-P - March 2012 109
Appendix
D
Two’s Complement Binary Numbers
The 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 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.