The only possible values are 0 or 1 , (True or False)•Boolean complementation which is analogous to Logical NOT•Boolean sum which is analogous to logical OR•Boolean product which is analogous to logical AND•

Boolean Algebra is an algebra similar to in concept to Propositional Logic

Given the correspondence with Propositional Logic, the following definitions are intuitive

1 + 1 = 1, 1 + 0 = 1, 0 + 1 = 1, 0 + 0 = 0.(Rosen 811)

1 · 1 = 1, 1 · 0 = 0, 0 · 1 = 0, 0 · 0 = 0.(Rosen 811)

Boolean Addition

Boolean Product

Boolean Complement

/0 = 1 , /1 = 0.(Rosen 811)

Note: A Boolean Expression can be constructed using multiple Boolean operators. The order of precedence follows from the corresponding logical operations

Example 1.11

Evaluate Boolean Expression: 1 · 0 + (0 + 1)

Example 1.12

Translate 1 · 0 + /(0 + 1) = 0 the equality found in Example 1, into a logical equivalence.

Solution: We obtain a logical equivalence when we translate each 1 into a T, each 0 into an F, each Boolean sum into a disjunction, each Boolean product into a conjunction, and each complementation into a negation.

We obtain

(T ∧ F) ∨ ¬(T ∨ F) ≡ F.(Rosen 812)

Logic Gates and Boolean Algebra Friday, August 18, 2017 3:00 PM

Math Methods Page 1

Observe the Boolean Identities mirror the corresponding logical identities …

Boolean Algebra provides a tool to study electronic switches and circuits!

Example 1.13

Find Boolean expressions that represent the functions F (x, y, z) and G(x, y, z), which are given in Table 1.(Rosen 819)

Logic Gates.

Identify each row in truth table where function is 1 1.Translate corresponding input combination to a logical conjunction (Boolean Product)

2.

Sum all such expressions.3.

Sum of Products Approach:

Math Methods Page 2

Boolean Algebra and Boolean Functions are often used to model electronic circuits and devices. Each Boolean Variable can be considered an input to the device and the function can be considered the output.

In fact, computers are built from implementations of logic devices called Logic Gates.

Their notated in circuit diagrams as follows:

Examples of more circuits!Can you draw the truth table corresponding to this circuit?

In class Exercise …Form into groups of 2 or 3.Design a circuit for the following function F

Math Methods Page 3

Math Methods Page 4