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Programming Logic Controllers

This chapter explores the fundamental number systems: decimal, binary, and hexadecimal. Each system's place value represents different powers—ten for decimal, two for binary, and sixteen for hexadecimal. Learn how to convert between these systems, including the use of prefixes such as 0x for hexadecimal and 0b for binary. We'll discuss the Binary Coded Decimal (BCD) format and Gray Code, a unique encoding system. Additionally, grasp the basics of binary arithmetic, including addition, multiplication, and division, as well as representations of fractions.

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Programming Logic Controllers

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  1. Programming Logic Controllers Number Systems and Codes - Chapter 3

  2. Decimal • Each “place” in the decimal system represents a power of ten • Hundred’s • Ten’s • One’s • Tenths • Hundredth’s

  3. Binary • Each “place” in the binary system represents a power of two • Four’s • Two’s • One’s • Half’s • Quarter’s

  4. Hexadecimal • Each “place” in the hexadecimal system represents a power of sixteen • 0 – 9 = 0 – 9 • A = 10 • B = 11 • C = 12 • D = 13 • E = 14 • F = 15

  5. Hexadecimal and Binary • Hex numbers can be preceded with 0x • Hex is a shorthand way of writing binary. • Each Hex digit is 4 binary digits • So hex 0x12 is binary 00010010 • So hex 0xAF is binary 10101111

  6. Octal • Each “place” in the octal system represents a power of eight • Each octal digit is 3 binary digits • Uses digits 0-7 • Some systems indicateoctal numbers using a leading 0 • Eg 023 = 010011 • Eg 075 = 111101

  7. Programming Notes Many programming environments allow you to specify literal constants in other than decimal formats. The following is one somewhat common syntax. 0x prefix indicates hexadecimal 0b prefixed indicate binary 0 prefix indicates octal

  8. Binary Coded Decimal - BCD • 4 bits represent a single decimal digit • Only 0 – 9 are valid • BCD 0111001100010010 = decimal 7312

  9. Gray Code • Special encoding system where two successive numbers are one “bit flip” apart • 00 = 0 • 01 = 1 • 11 = 2 • 10 = 3 • Special uses like optical encoders

  10. Binary Arithmetic Addition Subtraction Multiplication Division

  11. Binary Fractions • Hole around zero • Decimal .1 has no binary equivalent • 1/3 has no decimal equivalent (or binary) • 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + …

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