2. • An AND gate has this truth table when the
inputs are A and B, and the output is C:
• For an AND gate you multiply
the inputs to get the output
• So clearly we have:
• 0·0 = 0, and
• 1·1 = 1, and
• 0·1 = 0
• Which may be exactly what you expected.
3. • An OR gate has this truth table when the
inputs are A and B, and the output is C:
• For an OR gate you add
the inputs to get the output
• So clearly we have:
• 0 + 0 = 0, and
• 1 + 1 = 1, and
• 0+1=1
• Which this time may not be exactly what you
expected.
4. • Now, if you accepted what was claimed in
the previous slides, then you also have to
accept the following:
A·A = A
• Just let A be either zero or one and
remember the truth table for an AND.
• We also have:
A+A=A
• Again, just let A be either zero or one and
remember the truth table for an OR.
5. • Here is a truth table. It lists all possible
combinations for two variables.
• This truth table proves the following
theorem.
Theorem (de Morgan)
6. • One final note. There are some further
simple facts that come in useful. Note the
following:
• and:
