ICTE 123 Boolean Algebra Delali Kwasi Dake Lecturer

ICTE 123 – Boolean Algebra Delali Kwasi Dake Lecturer ICTE Department

Introduction �Boolean algebra is named after George Boole in 1854. �Major applications of Boolean algebra include: 1. Truth calculus 2. Switching algebra 3. Set theory (algebra of classes) 4. Design of circuits used in computers, calculators and host of devices controlled by microelectronics. �Boolean algebra is binary. �Objects can be one of two values: 1 or 0; true or false; high or low; positive or negative; closed or open; or any other pair of binary values. �The basic Boolean operations are AND, OR, and NOT.

Major Interpretations of Boolean Algebra

Main Concepts in Logic Gates �Logic Diagram �Truth Table �Boolean Expression �Combinational Gates

AND Gate �AND requires both input to be true for the result to be true. �The AND works like a pair of switches in series. Both switches must be closed for current to flow. �The AND gate in logic circuits looks like:

AND Gate �AND is considered to be Boolean multiplication and is represented by the middle dot symbol: · (such as A· B). A B Result 0 0 0 1 0 1 1 1

OR Gate �OR (or inclusive or) requires either object to be true for the result to be true. �The OR works like a pair of switches in parallel. Current will flow if either or both switches are closed. �The OR gate in logic circuits looks like

OR Gate �OR is considered to be Boolean addition and is represented by the plus symbol: + (such as (A+B). There is no Boolean subtraction operation. A B Result 0 0 0 1 0 1 1 1

NOT Gate �NOT (also called negation or complement) simply reverses the value of an object, changing true into false and changing false into true. �The NOT gate (or inverter) in logic circuits looks like:

NOT Gate �The truth table for the NOT Gate A result 0 1 1 0

NAND Gate �NAND is the combination of a NOT and an AND. NAND produces the opposite of an AND. The truth table for NAND (Not AND) is as follows: �The NAND gate in logic circuits looks like: A B Result 0 0 1 1 0

NOR Gate �NOR is the combination of a NOT and an OR. NOR produces the opposite of OR. The truth table for NOR (Not OR) is as follows: �The NOR gate in logic circuits looks like A 0 1 B Resul t 0 1 0 1 0

XOR Gate �XOR (or exclusive or) is similar A to the normal English meaning of the word “or” — a choice 0 between two items, but not both 1 or none. XOR is less commonly 0 written EOR. The symbol for the XOR operation is ⊕ 1 �The XOR gate in logic circuits looks like: B Result 0 0 0 1 1 0

XNOR Gate �XNOR (or NXOR) is the combination of a NOT and a XOR. XNOR produces the opposite of XOR. �The truth table for XNOR (Not e. Xclusive OR) is as follows: �The XNOR gate in logic circuits looks like: A B 0 1 0 0 1 1 Resul t 1 0 0 1

Combinational Gates

Combinational Gates

Assignment Find the Boolean Expression and the Truth Table

Combinational Gates