Notes on Computer Study

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  • Topic: Boolean logic, Logic gate, Boolean algebra
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  • Published : April 30, 2013
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Chapter 1.10 Logic Gates 1.10 (a) Function of AND, OR, NOT, NAND & NOR Logic gates and their input/output. Microprocessors are the central hardware that runs computers. There are several components that make a processor. The first is the transistor. Next, are logic gates where you put more than one transistor to work with others. The microprocessor works with binary arithmetic by using binary math to perform operations. When a microprocessor is designed, along with other design focus areas "Logic gate cell library (a library is collection of all low level logic functions like AND, OR and NOT etc.), which is used to implement the logic" is also deeply planned and developed. Logic gates carry out the instructions mathematical or otherwise that a processor performs, for example a logic gate performs a logical operation on one or more logic inputs and produces a single logic output. When you connect a variety of logic gates together, the results are circuits. The logic is called Boolean logic and is most commonly found in digital circuits. Following five logic gates are part of syllabus. 1. 2. 3. 4. 5. AND gate, OR gate, NOT gate, NAND gate, and NOR gate.

AND gate:

AND gate symbol The AND gate is a digital logic gate that behaves according to the table INPUT OUTPUT on your right. A HIGH output (1) results only if both the inputs to the A B A AND B (Q) AND gate are HIGH (1). If neither or only one input to the AND gate 0 0 0 is HIGH, a LOW output results. 0 1 0 1 0 0 1 1 1 Page 1 of 16

OR Gate:

OR gate symbol The OR gate is a digital logic gate that behaves according to the table on INPUT OUTPUT your right. A HIGH output (1) results if one or both the inputs to the gate A B A + B (Q) are HIGH (1). If neither input is HIGH, a LOW output (0) results. 0 0 0 0 1 1 1 0 1 1 1 1 NOT gate (Inverter):

NOT gate symbol In digital logic, an inverter or NOT gate is a logic gate which implements INPUT OUTPUT logical negation. Not gate represents perfect switching behavior. A NOT A 0 1 1 0 NAND gate:

NAND gate symbol The Negated AND, NO AND or NAND gate is the opposite of the digital AND gate, and behaves in a manner that corresponds to the INPUT OUTPUT opposite of AND gate, as shown in the truth table on the right. A LOW A B A NAND B (Q) output results only if both the inputs to the gate are HIGH. If one or 0 0 1 both inputs are LOW, a HIGH output results. 0 1 1 The NAND gate is significant because any Boolean function can be 1 0 1 implemented by using a combination of NAND gates. 1 1 0 Page 2 of 16

NOR gate:

NOR gate symbol The NOR gate is a digital logic gate that implements logical NOR - it behaves according to the truth table to the right. A HIGH output (1) results if both the inputs to the gate are LOW (0). If one or both input is HIGH (1), a LOW output (0) results. NOR is the result of the negation of the OR operator.

INPUT OUTPUT A B A NOR B (Q) 0 0 1 1 0 1 0 1 1 0 0 0

NAND and NOR are known as universal gates because they are inexpensive to manufacture and any Boolean function (AND, OR, NOT) can be constructed using only NAND or only NOR gates. Even NAND and NOR gates can be used as each other’s alternatives in a circuit.

NOR gate constructed using only NAND gates

NAND gate constructed using only NOR gates Page 3 of 16

1.10 (b)

Calculate outcome from a set of logic gates.

In this part 1.10 (b) we will explore the application of Boolean algebra in the design of electronic circuits. The basic elements of circuits are gates. Each type of gate implements a Boolean operation. Consider Boolean expression a(x)=x’; i.e., a(x) is the complement of x. Now a(0)=1 and...
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