Tugas 4 Bravo 2103015233 Gerbang Logika
Nama: Bravo
Marvel
Kelas: 2B
NIM:
2103015233
Rangkuman 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.
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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