1766-RM001A-EN-P MicroLogix 1400 Programmable Controllers ...

Appendix 26Number SystemsThis appendix:• covers binary and hexadecimal numbers.• explains the use of a hex mask to filter data in certain programminginstructions.Binary NumbersThe processor memory stores 16-bit binary numbers. As indicated in thefollowing figure, 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 avalue of 0; a 1 indicates the decimal value of the position. The equivalentdecimal value of the binary number is the sum of the position values.Positive Decimal ValuesThe far left position will always be 0 for positive values. As indicated inthe figure, this limits the maximum positive decimal value to 32767. Allpositions are 1 except the far left position.Other examples:0000 1001 0000 1110 = 2 11 +2 8 +2 3 +2 2 +2 1= 2048+256+8+4+2 = 23180010 0011 0010 1000 = 2 13 +2 9 +2 8 +2 5 +2 3= 8192+512+256+32+8= 9000661 Publication 1766-RM001A-EN-P - October 2008