Allen-Bradley SLC 500 Series - Page 652

Publication 1747-RM001G-EN-P - November 2008
F-4 Number Systems
Hexadecimal and binary numbers have the following equivalence.
Example
Decimal number -8586 in equivalent binary and hexadecimal form.
Hexadecimal number DE76 = 13x16
3
+14x16
2
+7x16
1
+6x16
0
= 56950. We
know this is a negative number because it exceeds the maximum positive value
of 32767. To calculate its value, subtract 16
4
(the next higher power of 16)
from 56950: 56950 - 65536 = -8586.
2x16
3
= 8192
1x16
2
= 256
8x16
1
= 128
10x16
0
= 10
2 1 8 A 8586
Hexadecimal 2 1 8 A = 8586
Binary 0 0 1 0 0 0 0 1 1 0 0 0 1 0 1 0 = 8586
8192
1x2
13
256
1x2
8
128
1x2
7
10
1x2
3
+1x2
1
Binary 1 1 0 1 1 1 1 0 0 1 1 1 0 1 1 0 = -8586
Hexadecimal D E 7 6 = 56950
(negative number, -8586)