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 indicate octal 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 + …