TUGAS 3. Gerbang logika dan aljabar boolean

Rezha Ramadhan Pratama

1703015094

Tugas 3. Rangkuman materi Aljabar Boolean

Gerbang Logika dan Aljabar Boolean

Aljabar Boolean adalah alat yang penting dalam menggambarkan, menganalisa, merancang, dan mengimplementasikan rangkaian digital.

Ø  Konstanta Boolean dan Variabel.

Aljabar Boolean dibawah ini hanya mempunyai dua nilai : 0 dan 1.

Logika 0 dapat dikatakan : false, off, low, no, saklar terbuka.

Logika 1 dapat dikatakan: true, on, high, yes, saklar tertutup.

Tiga operasi logika dasar: OR, AND, dan NOT.

Ø  Tabel Kebenaran

Sebuah tabel kebenaran menggambarkan hubungan antara input dan ouput sebuah rangkaian logika.

Jumlah The number of entries corresponds to the number of inputs. For example a 2 input table would have 2 2 = 4 entries. A 3 input table would have 2 3 = 8 entries

Ø  OR Operation with OR Gates

·       The Boolean expression for the OR operation is X = A + B

This is read as “x equals A or B.”

 X = 1 when A = 1 or B = 1.

·       Truth table and circuit symbol for a two input OR gate:

·  There are many examples of applications where an output function is desired when one of multiple inputs is activated.

 

     

Ø  AND Operations with AND gates

The Boolean expression for the AND operation is

X = A • B

This is read as “x equals A and B.”

x = 1 when A = 1 and B = 1.

Ø  Not Operation

·       The Boolean expression for the NOT operation is

X = A

This is read as:

X equals not A, or

X equals the inverse of A, or

X equals the complement of A

Truth table, symbol, and sample waveform for the NOT circuit.

Ø  Describing Logic Circuits Algebraically

·       The three basic Boolean operation (OR, NOT, AND) can describe any logic circuit.

·       If an expression contain both AND and OR gates the AND operation will be performed first, unless there is a parenthesis in the expression.

·     Example of Boolean expression for logic circuits:

 

Ø  Evaluating Logic Circuits Output

Rules for evaluating a Boolean expression:

1.     Perform all inversions of single terms.

2.     Perform all operations within parenthesis.

3.     Perform AND operation before an OR operation unless parenthesis indicate otherwise.

4.     If an expression has a bar over it, perform the operations inside the expression and then invert the result.

Output logic levels can be determined directly from a circuit diagram.

The output of each gate is noted until a final output is found.

Ø Implementing Circuits From Boolean Expression

It is important to be able to draw a logic circuit from a Boolean expression.

Ø  NOR Gates and NAND Gates

·       Combine basic AND, OR, and NOT operations.

·       The NOR gate is an inverted OR gate. An inversion “bubble” is placed at the output of the OR gate.

·       The NAND gate is an inverted AND gate. An inversion “bubble” is placed at the output of the AND gate.

·       The output of NAND and NOR gates may be found by simply determining the output of an AND or OR gate and inverting it.

·       The truth tables for NOR and NAND gates show the complement of truth tables for OR and AND gates.

Ø  Universality of NAND and NOR Gates

NAND or NOR gates can be used to create the three basic logic expressions (OR, AND, and INVERT)

This characteristic provides flexibility and is very useful in logic circuit design.

sumber : https://onlinelearning.uhamka.ac.id