3 - Number systems

Abstract

This chapter discusses the number systems used for a programmable logic controller (PLC). Computers, and hence PLC systems, are based on counting in twos—the binary system—because it is convenient for their system; their two digits being effectively just the off and on signals. When working with PLCs, other base number systems such as the octal system with base 8 can also be used. Octal or hexadecimal numbers are sometimes used to make numbers easier to handle and act as a half-way house between denary numbers and the binary numbers that computers work with. The octal system is based on eight digits—0, 1, 2, 3, 4, 5, 6, and 7. When a number is represented by this system, the digit position in the number indicates the weight attached to each digit, the weighting increasing by a factor of 8 proceeding from right to left. The hexadecimal system (hex) is based on 16 digits/symbols—0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, and F. When a number is represented by this system, the digit position in the number indicates that the weight attached to each digit increases by a factor of 16 proceeding from right to left.