ECT 464

1
ECT 464

• Lecture 2
• Binary Mathematics

2
A shut mouth gathers no foot.

• He who guards his lips guards his life,       
  but he who speaks rashly will come to ruin.
  Proverbs 133

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Number Systems

• 0 or 1 0-7 0-F 0-?
• Binary Octal Hexadecimal Decimal
• 0000 000 0 0
• .. .
• 1111B 17O FH 15

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Binary to Decimal Conversion

• Add the columns with 1s in them
• Example
• Convert 10110B to Decimal
• 16 8 4 2 1
• 1 0 1 1 0
• 16 4 2 22D

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Binary to Octal Conversion

• Group the columns into groups of three and count
  from 0-7.
• Example
• Convert 1011100110B to Octal
• 1 011 100 110
• 1 3 4 6
• 1346O

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Binary to Hexidecimal Conversion

• Group the columns into groups of four and count
  from 0-F.
• Example
• Convert 1011100110B to Hex
• 10 1110 0110
• 2 E 6
• 2E6H

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Decimal to Binary Conversion

• Subtract column values from Decimal value
• Example
• Convert 21D to Binary
• 32 16 8 4 2 1
• 1 0 1 0 1

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Decimal to Octal Conversion

• Subtract column values from Decimal value
• Example
• Convert 87D to Octal
• 64 8 1
• 1 2 7
• 127O

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Decimal to Hexadecimal Conversion

• Subtract column values from Decimal value
• Example
• Convert 287D to Hex
• 256 16 1
• 1 1 F
• 11FH

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Binary Addition

• A carry is needed anytime the sum is
• greater than one.
• Example
• 1010
• 0111
• 10001

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Binary Subtraction

• Twos Complement seems to be the easiest to
  understand. Complement and add 1.
• Example 00001
• 10011 10011
• - 01010 10101
• 1001 01001

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Logical NOT

• F NOT A
• If A 0, F 1
• If A 1, F 0

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Logical AND

• F A AND B
• Both A and B have to be one for F to be one. If
  either or both are zero, F is zero.
• A B F
• 0 0 0
• 0 1 0
• 1 0 0
• 1 1 1

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Logical OR

• F A OR B
• Either A or B or both have to be one for F to be
  one. If both are zero, F is zero.
• A B F
• 0 0 0
• 0 1 1
• 1 0 1
• 1 1 1

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Logical XOR

• F A XOR B
• Only A or B, not both, have to be one for F to be
  one. If both are zero or one, F is zero.
• A B F
• 0 0 0
• 0 1 1
• 1 0 1
• 1 1 0

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Next Class

• PLC Selection
• Basic Ladder Logic
• Input/Output Logic and Wiring