Minterms, Maxterms
Objectives
We would like to :
- Discuss Minterms
- Discuss Maxterms
Notes
- This is Carpineli chapter 2.2
- Eventually we want to find a way to optimize a function we created in a truth table.
- We use two possible expressions to do this.
- A sum of products
- A product of sums
- Minterms are used in the sum of products
- Consider the two input possibilities
| a | b | Minterm | Notation 1 | Notation 2 |
|---|
| 0 | 0 |
a · b |
m0 | 0 |
| 0 | 1 |
a · b |
m1 | 1 |
| 1 | 0 |
a · b |
m2 | 2 |
| 1 | 1 |
a · b |
m3 | 3 |
- It is easy to see how we can
- Read the minterm from the table
- If the input value is a 1, keep the symbol
- If the input value is a 0, write the inverse of the symbol.
- It also make sense that each minterm contributes one bit to the final answer
- So we just add them together to get the equation.
- Form the sum of products expression using minterms for a number of tables.
- Maxterms are used in the product of sums.
- In my mind these are harder, but they are just the inverse.
- Minterms are produced where the table has a 1, Maxterms are produced where the table has a 0
- Minterms are what makes the expressions 1, maxterms are what makes the expression 0.
-
| a | b | Maxterm |
|---|
| 0 | 0 |
a + b | M0 |
| 0 | 1 |
a + b | M1 |
| 1 | 0 |
a + b | M2 |
| 1 | 1 |
a + b | M3 |
- Reading the maxtersm is looking for 0 in the final output
- And these togeher.
-
| a | b | F(a,b) | Term |
|---|
| 0 | 0 | 0 | M0 |
| 0 | 1 | 1 | m1 |
| 1 | 0 | 1 | m2 |
| 1 | 1 | 0 | M3 |
- SO the expression is either m1 + m2 or M0·M3
- In the end, we can build an expression out of either, just pick the one with the fewer entries?
- Let's play with our old friend the pass the vote indicator.
- Carpineli notes