In Recent Modern computers do not operate with decimal numbers. What the computer processes are binary numbers, numbers represented by 0 and 1. In digital systems these two numbers are generated in the form of voltage levels, which are then used to operate logic gates. The logic gate itself basically consists of basic components such as transistors, resistors and diodes, which are integrated in one series (IC).
The three basic logic gates are OR , AND, and NOT .
This gate if strung together to form a so-called logic circuit function.
The discuss is the logic circuits and the concepts needed to understand them.
This example is a circuit that uses Boolean expressions:
Figure 1 The combination circuit of AND and OR gates
From Figure 1 the output uses AND and OR operations X=AB+C, in this case the AND operation is performed first (AB ). Likewise for the second form X=(A+B)+C : (A+B) is solved first.
Circuits containing Inverters
Whenever inventers appears in a logic circuit, its output is the same as the input and is marked with an inverse above it.
Figure 2 Inverter application circuit
In this case, the inverter output becomes A’, then complete the expressions for AND and OR output starting from front to back.
Evaluation of Logic Circuit Output
If a Boolean expression of a logic circuit output has been obtained, the output can be evaluated by assigning a value to the input.
X = A’BC (A+D)’
If A=0, B=1, C=1, D=1
X = A’BC (A+D)’
= 0’*1* 1* (0+1)’
= 1 *1*1* (1)’
= 1 *1*1* 0
And If A=0, B=0, C=1, D=1, E= 1 is given in the equation below: Then we get:
X = [D+ ((A+B)C)’] * E
= [1 + ((0+0)1 )’] * 1
= [1 + (0*1 )’] * 1
= [1+ 0′] *1
= [1+ 1 ] * 1
General rules for evaluating Boolean expressions:
- First, perform all inversions; that is, 0 = 1 or 1 = 0. 2. Perform all the operations in brackets.
- Perform the A!D operation before the OR operation.
- If the expression has a bar above it, first make the whole equation and then mark the bar (reversal).
Determining the output level of a logic diagram
The logic level of the output of a logic diagram can also be determined directly without using Boolean expressions.
Figure 3 Circuit with Boolean Equation
Figure 4 Circuit Without Equation
Figure 3 above is equipped with Boolean logic equations, on the other hand Figure 4 is evaluated directly by assigning logical values to its inputs. Consider Figure 4, if A=0, B=C=D=1, we get X=0.
Logical Circuit Implementation of Boolean Expression
If the operation of a logic circuit is given in Boolean expression, then we can directly describe the logic circuit. For example, let’s say we want to create a logical circuit from the Boolean expression y = AC+BC’ + A’BC. This equation has three variables (AC, BC’, A’BC), which are ORed together. The three variables are the output of AND (AC= AC, BC’=B. C’, and A’BC= A’.BC), which are then ORed. Note that a NOT gate is required to obtain the inversions (A’ and C’) in the equation. The first step is to describe the last output (OR operation) and obtain a logic circuit as shown in Figure 5 (a) Next, the front section begins by reversing all inputs to be reversed, then
describes the AND operation, and finally the output of each gate is connected and a logic circuit is obtained as Figure 5 (b).
Figure 5 Logical circuit of Boolean expressions
- With the logical symbols AND, OR, NOT, NAND, NOR, EX_OR an EX-NOR can be made a system that works digitally
2. To test the output of a circuit logic, can be done by directly providing a logic 1 or logic 0 at the input terminal or by going through a logic equation.