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 22 = 4 entries. A 3 input table would have 23 = 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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