Digital electronics

Digital electronics

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  BMT 2013 MUHAMMAD SYAHRULFIKRI B AHMAD MUHAMMAD MUNZIR HAKIMI B JAFAR SHAHRIR IRWAN B MOHAMMAD NANI SHAJIEHA BT ZAWAWI
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   Digital electronics,or digital (electronic) circuits, are electronics that represent signals by discrete bands of analog levels , rather than by continuous ranges (as used in analog electronics).  All levels within a band represent the same signal state.  In most cases the number of these states is two, and they are represented by two voltage bands - one near a reference value (typically termed as "ground" or zero volts) -and the other a value near the supply voltage. These correspond to the "false" ("0") and "true" ("1") values of the Boolean domain, respectively, yielding binary code .
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   Has ahigh output only when all its inputs are high .  * when all inputs are low (0), the output is low. The only way to get a high output (1) is to raise all inputs to a high state.
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   An ORGATE has two or more input signals but only one output signal. It is called an OR GATE because the output is high if any or all the input are high.
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   The NANDGATE can have two or more input but only has only one input.
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   The NORcan have two or more input but only has only one input.  If no specific NOR gates are available, one can be made from NAND gates, because NAND and NOR gates are considered the "universal gates", meaning that they can be used to make all the others.
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   An XORis a 2-input gate that is similar in output to an OR GATE except that the XOR produces a 0 output when both input are 1.
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   Boolean Algebra– Switching Algebra • It must be carefully noted that symbols l or 0 representing the truth-values of the Boolean variable, have nothing to do with numeric 1 and 0 respectively. In fact these symbols may be used to represent the active and passive states of a component say a switch or a transistor in an electric circuit.
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   Boolean algebraa digital circuit is represented by a set of input and output signals and the function of the circuit is suppressed as a set of Boolean relationship between the symbols. Boolean logic deals with only two variables, 1 for ‘True’ and 0 for ‘false’.
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   i) UsingOR operation the Law is given as –  A + B = B + A  By this Law order of the OR operations conducted on the variables makes no differences.  This law using AND operation is –  A.B = B.A  This mean the same as previous the only difference is here the operator is (.). Here the order of the AND operation conducted on the variables makes no difference. This is an important law in Boolean algebra.
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   This lawis given as –  A+(B+C) = (A+B)+C  This is for several variables, where the OR operation of the variables result is same though the grouping of the variables. This law is quite same in case of AND operator. It is  A.(B.C) = (A.B).C  Thus according to this law grouping of Boolean expressions do not make any difference during the AND operation of several variables. Though but these laws are also very important
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  Among the lawsof Boolean algebra this law is very famous and important too. This law is composed of two operators. AND and OR. The law is  A + BC = (A + B)(A + C)  Here the logic is, AND operation of several variables and then the OR operation of the result with a single variable is equivalent to the AND of the OR of single variable to one of the variable of several variables to make it simple, set BC be the several variables then A will be OR with B. Firstly and again A will be OR with C, then the result of the OR operation will be AND. The proof of this law in Boolean algebra is given below :-  Proof A + BC = A.1 + BC [ Since, A.1 = A] = A(1 + B) + BC [Since, B+1 = 1] = A.1 + AB + BC = A.(1 + C) + AB + BC [Since, A.A = A.1 = A] = A (A + C) + B (A+C) A+BC = (A+B)(A+C) This law can also be for Boolean multiplication. Such as – A.(B + C) = A.B + A.C
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   In lawsof Boolean algebra there are several groups of laws. Absorption laws are such a group of laws. The laws and their respective proves are given below. i) A+AB = A Proof. A+AB = A.1 + AB [A.1 = A] = A(1+B) [Since, 1 + B = 1] = A.1 = A ii) A(A+B) = A Proof. A(A+B) = A.A + A.B = A+AB [Since, A.A = A] = A(1+B) = A.1 = A
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  Digital logic circuitsare often classified into two very broad categories : combinational logic circuits and sequential logic circuits. Generally, a circuits is considered a combinational logic if its output goes either low or high with a specified combination of input signals. The order or sequence in which the inputs are applied is not important. In digital circuits, with the help of the software associated with the underlying digital circuit we can easily change the functionality of the digital circuit without changing the actual circuit. These circuits are generally referred to as programmable digital circuits