Gerbang Logika dan Aljabar Boolean
* Aljabar Boolean adalah alat yang penting dalam menggambarkan, menganalisa, merancang, dan mengimplementasikan rangkaian digital.
- Aljabar Boolean dibawah ini hanya mempunyai dua nilai : 1 dan 0
- 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 output sebuah rangkaian logika.
* Jumlah The number of entries corresponds to the number of inputs. For example
a 2 input table waould have 2^2 = 4 entries.
A 3 input table would have 2^3 = 8 entries
* Contoh tabel kebenaran dengan masukan 2, 3, dan 4 buah
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.
* Truth table and circuit symbol for a two input OR gate :
* The OR operation is similiar to addition but when A = 1 and B = 1, the OR operation produce 1 + 1 = 1
* 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)
* There are many examples of applications where an output fuction is desire when one multiple input is activated
* The AND operation is similiar to multiplication
* In the Boolean expresion
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
* 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.
Describing Logic Circuits Algebraically
* The three basic Boolean operation ( 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
* Examples of Boolean expressions for logic circuits
* Examples using inverters
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
Evaluating Logic Circuit Outputs
* Evaluate Boolean expressions by substituting values and performing the indicated operations
Implementing Circuits From Boolean Expressions
* It is important to be able to draw a logic circuit from a Boolean expression
* The expression
X = A. B. C
could be drawn as a three input AND gate
* a more complex example such as
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
* 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 
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
* Combinations of NANDs are used to creat the three logic functions
* Combinations of NORs are used to creat the three logic functions
IEEE/ANSI Standard Logic Symbols
* These symbols are not widely accepted but may appear in some schematics
Application
Sumber artikel
Nama : Rafi Fadhlur Rahman
NIM : 2003015221
Kelas : 2F
No comments:
Post a Comment