Tugas 4 [Dwi Nita Maulida] Gerbang Logika

 GERBANG LOGIKA DAN ALJABAR BOOLEAN 

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.

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 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.

Truth table and circuit symbol for a two input OR gate:

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).

OR Operation With OR Gates

There are many examples of applications where an output function is desired when one of multiple inputs is activated.

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

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

This Is read as: X=A

x equals NOT A, or x equals the inverse of A, or x equals the complement of A

NOT Operation

Truth table, symbol, and sample waveform for the NOT circuit.

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.

Describing Logic Circuits Algebraically 

Describing Logic Circuits Agebraically

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.

Evaluating Logic Circuit Outputs

Evaluate Boolean expressions by substituting values and performing the indicated operations:

A = 0, B =1, C =1, and  D =1

Evaluating Logic Circuit Outputs

Output logic levels can be determined directly from a circuit diagram.

The output of each gate is noted until a final output is found

a final output is found.

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

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