Tugas 3. Rangkuman Materi Gerbang Logika dan Aljabar Boolean

 Gerbang Logika dan Aljabar Boolean

Sekarang kita telah mengetahui konsep bilangan biner dan kita akan mempelajari cara menggambarkan bagaimana sistem menggunakan level logika biner dalam membuat keputusan. Aljabar Boolean adalah alat yang penting dalam menggambarkan, menganalisa, merancang, dan mengimplementasikan rangkaian digital.

Konstanta Boolean dan Variable

• Aljabar Boolean dibawah ini hanya mempunyai 2 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 output sebuah rangkaian logika.
• Jumlah the number of entries corresponds to the number of input. 

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 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).

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 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

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.
• 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 unless parenthesis indicate otherwise.
• 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.

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.

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.

IEEE/ANSI Standard Logic Symbols

• Compare the IEEE/ANSI symbols to traditional symbols. 
• These symbols are not widely accepted but may appear in some schematics.

Summary of Methods to Describe Logic Circuits

• The three basic logic functions are AND, OR, and NOT.  
• Logic functions allow us to represent a decision process. 
• If it is raining OR it looks like rain I will take an umbrella.
• If I get paid AND I go to the bank I will have money to spend.

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