Programming Logic Controllers

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# Programming Logic Controllers - PowerPoint PPT Presentation

Programming Logic Controllers. Number Systems and Codes - Chapter 3. Decimal. Each “place” in the decimal system represents a power of ten Hundred’s Ten’s One’s Tenths Hundredth’s . Binary. Each “place” in the binary system represents a power of two Four’s Two’s One’s Half’s

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### Programming Logic Controllers

Number Systems and Codes - Chapter 3

Decimal
• Each “place” in the decimal system represents a power of ten
• Hundred’s
• Ten’s
• One’s
• Tenths
• Hundredth’s
Binary
• Each “place” in the binary system represents a power of two
• Four’s
• Two’s
• One’s
• Half’s
• Quarter’s
• 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
• 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
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
Programming Notes

Many programming environments allow you to specify literal constants in other than decimal formats. The following is one somewhat common syntax.

0b prefixed indicate binary

0 prefix indicates octal

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