B - number systems, hex mask, Binary numbers, Positive decimal values – Rockwell Automation 1747-PT1, D1747NP002 Hand-Held Terminal User Manual
Page 449: Number systems, hex mask
B
Appendix
B–1
Number Systems, Hex Mask
This appendix:
•
describes the different number systems you need to understand for use of
the HHT with SLC 500 family controllers
•
covers binary, Binary Coded Decimal (BCD), and hexadecimal.
•
explains the use of a Hex mask used to filter data in certain programming
instructions
The processor memory stores 16-bit binary numbers. As indicated in the
figure below, 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 at that position; 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.
1x2
14
= 16384
1x2
13
= 8192
1x2
12
= 4096
1x2
11
= 2048
1x2
10
= 1024
1x2
9
= 512
1x2
8
= 256
1x2
7
= 128
1x2
6
= 64
1x2
5
= 32
1x2
4
= 16
1x2
3
= 8
1x2
2
= 4
1x2
1
= 2
1x2
0
= 1
1
0
1 1
1
1
1 1
1
1
1 1
1
1
1 1
16384
8192
4096
2048
1024
512
256
128
64
32
16
8
4
2
1
32767
0x2
15
= 0
This position is always zero for positive numbers.
+
The binary number may also be converted to decimal as follows:
16 bit pattern = 0111111111111111
2
=
2
14
+ 2
13
+ 2
12
+ 2
11
+ 2
10
+ 2
9
+ 2
8
+ 2
7
+ 2
6
+ 2
5
+ 2
4
+ 2
3
+ 2
2
+ 2
1
+ 2
0
= 16384
+
8192
+
4096
+
2048
+
1024
+
512
+
256
+
128
+
64
+
32
+
16
+
8
+
4
+
2
+
0
= 32767
Binary Numbers