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.
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