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

662 Number Systems1x2 14 = 163841x2 13 = 81921x2 12 = 40961x2 11 = 20481x2 10 = 10241x2 9 = 5121x2 8 = 2561x2 7 = 1281x2 6 = 641x2 5 = 321x2 4 = 161x2 3 = 81x2 2 = 41x2 1 = 21x2 0 = 10 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 327670x2 15 = 0 This position is always zero for positive numbers.Negative Decimal ValuesThe 2s complement notation is used. The far left position is always 1 fornegative values. The equivalent decimal value of the binary number isobtained by subtracting the value of the far left position, 32768, from thesum of the values of the other positions. In the following figure, the valueis 32767 - 32768 = -1. All positions are 1.Another example:1111 1000 0010 0011 =(2 14 +2 13 +2 12 +2 11 +2 5 +2 1 +2 0 ) - 215 =(16384+8192+4096+2048+32+2+1) - 32768 =30755 - 32768 = -2013.An often easier way to calculate a value is to locate the last 1 in the stringof 1s beginning at the left, and subtract its value from the total value ofpositions to the right of that position. For example,1111 1111 0001 1010 = (24+23+21) - 28 = (16+8+2) - 256 = -230.Publication 1766-RM001A-EN-P - October 2008