Rockwell Automation 1762-IT4 Thermocouple/mV Input Module - Manual (Page 99)

1 Publication 1762-UM002A-EN-P - July 2002
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
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.