Rockwell Automation 1790P-4R0 CompactBlock LDX I/O RTD/Resistance Input Module - Manual (Page 55)

1 Publication 1790-UM002A-EN-P
Appendix
B
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 RTD/resistance module 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.
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