7 February, 2000

Logic design -- Getting the homework done

Truth tables
Cannonical sum-of-products
Algebraic simplification

Everyone's favorite example -- the seven segment display

 _         _    _         _    _    _    _    _    _         _         _    _
| |    |   _|   _|  |_|  |_   |_     |  |_|  |_|  |_|  |_   |     _|  |_   |_ 
|_|    |  |_    _|    |   _|  |_|    |  |_|   _|  | |  |_|  |_   |_|  |_   |

Laws of Boolean Algebra

Commutativity	`x` + `y` = `y` + `x`	`x` `y` = `y` `x`
Associativity	`x` + (`y` + `z`) = (`x` + `y`) + `z`	`x` (`y` `z`) = (`x` `y`) `z`
Distributivity	`x` (`y` + `z`) = `x` `y` + `x` `z`	`x` + `y` `z` = (`x` + `y`) (`x` + `z`)
Identity	`x` + 0 = `x`	`x` 1 = `x`
Idempotency	`x` + `x` = `x`	`x` `x` = `x`
Annihilation	`x` + 1 = 1	`x` 0 = 0
Complement	`x` + `x`' = 1	`x` `x`' = 0
Involution	(`x`')' = `x`
de Morgan's law	(`x` + `y`)' = `x`' `y`'	(`x` `y`)' = `x`' + `y`'
absorption	`x` + `x` `y` = `x`	`x` (`x` + `y`) = `x`