Tugas 4 Arfan 210301508 Gerbang Logika

Gerbang logika

Gerbang Logika dan Aljabar Boolean

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

Konstanta Boolean dan Variabel

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

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

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

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

Tabel Kebenaran

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

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

Gerbang Logioka

Operasi OR dengan gerbang OR

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

 

OR Operation With OR Gates

l  The OR operation is similar to addition but  when A = 1 and B = 1, the OR operation  produces 1 + 1 = 1.

l  In the Boolean expression

             x=1+1+1=1

             We could say in English that x is true (1) when A is true

             OR B is true (1) OR C is true (1).

Operation With AND Gates

l  The AND operation is similar to multiplication.

l  In the Boolean expression

             X = A • B • C

             X        = 1 only when A = 1, B = 1, and C = 1.

NOT Operation

l  The Boolean expression for the NOT  operation is

                                                             X = A

l  This is read as:

l  x equals NOT A, or

l  x equals the inverse of A, or

l  x equals the complement of A

Describing Logic Circuits  Algebraically

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

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

 

Evaluating Logic Circuit Outputs

l  Rules for evaluating a Boolean expression:

l  Perform all inversions of single terms.

l  Perform all operations within parenthesis.

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

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

Evaluating Logic Circuit Outputs

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

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

Implementing Circuits From  Boolean Expressions

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

l  The expression

                                                                 x = A ×B×C

could be drawn as a three input AND gate.

l  A more complex example such as

y = AC + BC + ABC

could be drawn as two 2-input AND gates and one 3-input  AND gate feeding into a 3-input OR gate. Two of the AND  gates have inverted inputs.

NOR Gates and NAND Gates

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

l  The Boolean expression is

                                                            x = AB

 

NOR Gates and NAND Gates

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

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

Universality of NAND and NOR Gates

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

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

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