A) Boolean Expressions à Truth tables

Algorithm:

  1. Analyse the boolean expression and decide how many entries will be in the truth table
  2. Fill in all the initial entries
  3. Put paranthesis for each level
  4. Begin with the innermost expression; evaluate and build its truth table
  5. Continue with next innermost expression
  6. Done when there is only one value

B) Logic Circuits à Truth tables

Rules:

  1. Input to a gate is on its left, output is to its right
  2. An output of a gate, is the input to the gate on its right
  3. Input values for the circuit are at the left-most
  4. Output of the right-most gate(s) is the circuit output for a particular set of input values
Algorithm:
  1. Analyse the logic circuit and decide how many entries will be in the truth table
  2. Fill in all the initial entries
  3. Start from left-most gates of the circuit
  4. Work from left to right
  5. For each gate you encounter build its truth table based on its input
  6. Continue with step 4 until you get to the out of the right-most gate of the circuit
C) Boolean Expressions à Logic Circuits
  1. Start with outer-most Boolean expression and work towards the inner-most
  2. Build the corresponding circuit:
    1. Draw the gate that correspond to the Boolean operator
    2. The output of a gate is the input of the gate on its right (which correspond to the outer Boolean expressions)
    3. The out-most of the Boolean expression is the right-most gate (output)
    4. The inner-most Boolean expressions are the left-most gates (inputs)
    5. Order and position do not matter but we want to make it easy to read
D) Logic Circuits à Boolean Expressions
  1. Solve the circuit from the right-most gate (output) and work back (to the left)
  2. Build the corresponding Boolean expression from the out-most to inner-most level:
    1. The right-most gate (the output) is the outer-most operator of the Boolean Expression
    2. The left-most gates (inputs) are the inner-most operators of the Boolean expression
    3. The inputs of the circuits are the variables of the Boolean expression
    4. Write the Boolean operator that correspond to the gate. Put paranthesis for the inner expression (inputs of the gate)
    5. Order and position do not matter but we want to make it easy to read

E) Truth Table à Logic Circuits and Boolean Expressions

  1. For all the inputs in a row whose output is 1:
    1. If input P value is 1 then write P
    2. If input P value is 0 then write NOT P
    3. Connect then all the inputs in the row with AND gates
  2. Repeat for all the rows in the truth table
  3. Connect the rows with OR gates

Application: How to build a logic circuit which adds two binary digits.