EET3370 -- Programmable Logic Controller Basics

Number Systems Used in PLC's

Weighted Number Systems

B^N . . . . B⁴ B³ B² B¹ B⁰ . B^-1 B^-2 B^-3 B^-4 (B^-N)

P_N P₄ P₃ P₂ P₁ P₀ . P_-1 P_-2 P_-3 P_-4 (P_-N)

B = Base P = Position

Decimal

10^N . . . .10⁴ 10³ 10² 10¹ 10⁰ . 10^-1 10^-2 10^-3 10^-4 (10^-N)

P_N P₄ P₃ P₂ P₁ P₀ . P_-1 P_-2 P_-3 P_-4 (P_-N)

Value 10000 1000 100 10 1 1/10 1/100 1/1000 1/10000

Binary

2^N . . . . 2⁴ 2³ 2² 2¹ 2⁰ . 2^-1 2^-2 2^-3 2^-4 (2^-N)

P_N P₄ P₃ P₂ P₁ P₀ . P_-1 P_-2 P_-3 P_-4 (P_-N)

Value 16 8 4 2 1 1/2 1/4 1/8 1/16

Octal

8^N . . . . 8⁴ 8³ 8² 8¹ 8⁰ . 8^-1 8^-2 8^-3 8^-4 (8^-N)

P_N P₄ P₃ P₂ P₁ P₀ . P_-1 P_-2 P_-3 P_-4 (P_-N)

Value 4096 512 64 8 1 1/8 1/64 1/512 1/4096

Hexidecimal

16^N . . . .16⁴ 16³ 16² 16¹ 16⁰ . 16^-1 16^-2 16^-3 16^-4 (16^-N)

P_N P₄ P₃ P₂ P₁ P₀ . P_-1 P_-2 P_-3 P_-4 (P_-N)

Value 65536 4096 256 16 1 1/16 1/256 1/4096 1/65536

Binary, Octal, Decimal, and Hexadecimal Equivalents

Binary Oct. Dec Hex

- 0000 000 0 0000

* 0001 001 1 0001

** 0010 002 2 0002

*** 0011 003 3 0003

**** 0100 004 4 0004

***** 0101 005 5 0005

****** 0110 006 6 0006

******* 0111 007 7 0007

******** 1000 010 8 0008

********* 1001 011 9 0009

********** 1010 012 10 000A

*********** 1011 013 11 000B

************ 1100 014 12 000C

************* 1101 015 13 000D

************** 1110 016 14 000E

*************** 1111 017 15 000F

**************** 10000 020 16 0010

Conversions

Changing octal to binary and binary to octal using three bit groups example.

Changing hexadecimal to binary and binary to hexadecimal using 4 bit groups example.

Storing Numbers in Machine Language

Stored positive examples.

Storing and retrieving negative numbers.

Stored negative examples.