Allen-Bradley MicroLogix 1200 User Manual page 81

Positive Decimal Values
1
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
15
at the left with 2 . 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.
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:
11+
0000 1001 0000 1110 = 2
13+
0010 0011 0010 1000 = 2
14
1 x 2
1 x 2
0 1 1 1
15 This position is always 0 for positive numbers.
0 x 2 = 0
8+ 3+ 2+ 1
2 2 2 2 = 2048+256+8+4+2 = 2318
9+ 8+ 5+ 3
2 2 2 2 = 8192+512+256+32+8 = 9000
= 16384
13
= 8192
12
1 x 2 = 4096
11
1 x 2 = 2048
10
1 x 2 = 1024
9
1 x 2 = 512
8
1 x 2 = 256
7
1 x 2 = 128
6
1 x 2 = 64
1 x 2 = 32
1 1 1 1 1 1 1 1
Publication 1762-UM003A-EN-P - February 2003
C
Appendix
0
and ending
16384
8192
4096
2048
1024
512
256
128
64
5
32
4
1 x 2 = 16 16
3
1 x 2 = 8
8
2
1 x 2 = 4 4
1
1 x 2 = 2 2
0
1 x 2 = 1 1
32767
1 1 1 1