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

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

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 So hex 0xAF is binary

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 indicate octal numbers using a leading 0 Eg 023 = Eg 075 =

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

Binary Coded Decimal - BCD 4 bits represent a single decimal digit Only 0 – 9 are valid BCD = 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 Addition Subtraction Multiplication Division

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 + …