Tugas 4 Muchlas 2103015057 Gerbang Logika

Konstanta Boolean dan Variabel. Aljabar

 Boolean 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

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.

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. The OR operation is similar to addition but when A = 1 and B = 1, the OR operation produces 1 + 1 = 1. In the Boolean expression In the Boolean expression x=1+1+1=1 We could say in English that x is true (1) when A is true (1) OR B is true (1) OR C is true (1).

OR Operation With OR Gates There are many examples of applications where an output function is desired when one of multiple inputs is activated

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.  Truth table and circuit symbol for a two input AND gate are Truth table and circuit symbol for a two input AND gate are shown. Notice the difference between OR and AND gates.

Operation With AND Gates The AND operation is similar to multiplication. In the Boolean expression X = A • B • C X = 1 only when A = 1, B = 1, and C = 1

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

Describing Logic Circuits Algebraically The three basic Boolean operations (OR, AND, NOT) can describe any logic circuit. If an expression contains both AND and OR gates the AND operation will be performed first, unless there is a parenthesis in the expression.

Describing Logic Circuits Algebraically The output of an inverter is equivalent to the input with a bar over it. Input A through an inverter equals A.

Evaluating Logic Circuit Outputs Rules for evaluating a Boolean expression: Perform all inversions of single terms. Perform all operations within parenthesis. Perform AND operation before an OR operation  Perform AND operation before an OR operation unless parenthesis indicate otherwise. If an expression has a bar over it, perform the operations inside the expression and then invert the result.

Evaluating Logic Circuit Outputs
Output logic levels can be determined directly from a circuit diagram. The output of each gate is noted until a final The output of each gate is noted until a final output is found.

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 Boolean expression is, x = A + B

NOR Gates and NAND Gates The NAND gate is an inverted AND gate. An inversion “bubble” is placed at the output of the AND gate. The Boolean expression i The Boolean expression is x = AB

NOR Gates and NAND Gates 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 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 NAND or NOR gates can be used to create the three basic logic expressions (OR, AND, and INVERT) This characteristic provides flexibility and is This characteristic provides flexibility and is very useful in logic circuit design.

Sumber Berita :

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