Puertas

PHYSICS PROJECT

Sanchit Karve born2c0de born2c0de@hotmail.com

ADDING TWO 2-BIT NUMBERS USING A BINARY FULL ADDER

CONTENTS

1. INTRODUCTION 2. ADDING BINARY NUMBERS 3. AIM 4. APPARATUS 5. PROCEDURE 6. CIRCUIT DIAGRAM 7. TRUTH TABLE 8. CONCLUSION 9. REFERENCES

INTRODUCTION
If you look at the history of computer technology, the Boolean Gate has remained a constant component of thecomputer. The technologies used to implement those gates, however, have changed dramatically over the years. The very first electronic gates were created using relays. These gates were slow and bulky. Vacuum tubes replaced relays. Tubes were much faster but they were just as bulky, and they were also plagued by the problem that tubes burn out (like light bulbs). Once transistors were perfected(transistors were invented in 1947), computers started using gates made from discrete transistors. Transistors had many advantages: high reliability, low power consumption and small size compared to tubes or relays. These transistors were discrete devices, meaning that each transistor was a separate device. Each one came in a little metal can about the size of a pea with three wires attached to it.It might take three or four transistors and several resistors and diodes to create a gate. In the early 1960s, integrated circuits (ICs) were invented. Transistors, resistors and diodes could be manufactured together on silicon "chips." This discovery gave rise to SSI (small scale integration) ICs. An SSI IC typically consists of a 3-mm-square chip of silicon on which perhaps 20 transistors andvarious other components have been etched. A typical chip might contain four or six individual gates. These chips shrank the size of computers by a factor of about 100 and made them much easier to build.

The devices used in digital circuits operate in ON and OFF state. It can also be represented as HIGH and LOW or 1 and 0 respectively. Since a digital system can have only one of the two states 1and 0, the binary system is used to design them. The two states can also be designated as TRUE or FALSE. George Boole introduced the concept of binary system in the study of mathematical theory of logic and developed what is now known as Boolean Algebra. GATES are the most basic digital devices. A gate has one or more than one input and produces an output that is a function of the current inputvalue(s). Irrespective of the complexities of a digital system, only a few basic operations can be performed which are AND, OR and NOT.

The Adder is a digital circuit which forms the sum and carry of two or more numbers. Adder circuits are essential inside microprocessors as part of the ALU, or arithmetic logic unit, where the processing and manipulation of binary numbers takes place. It usesthree gates XOR, AND and OR to perform addition.

AND Gate
The AND gate performs a logical "and" operation on two inputs, A and B:
AND Gate A 0 0 1 1 B 0 1 0 1 Q 0 0 0 1

The idea behind an AND gate is, "If A AND B are both 1, then Q should be 1." You can see that behavior in the logic table for the gate. You read this table row by row, like this:
AND Gate A 0 0 1 1 B 0 1 0 1 Q 0 0 0 1 If Ais 0 AND B is 0, Q is 0. If A is 0 AND B is 1, Q is 0. If A is 1 AND B is 0, Q is 0. If A is 1 AND B is 1, Q is 1.

OR Gate
The next gate is an OR gate. Its basic idea is, "If A is 1 OR B is 1 (or both are 1), then Q is 1."
OR Gate A 0 0 1 1 B 0 1 0 1 Q 0 1 1 1

XOR Gate
The XOR gate is also known as "exclusive or".
XOR Gate A 0 0 1 1 B 0 1 0 1 Q 0 1 1 0

The idea behind an XOR gate is,"If either A OR B is 1, but NOT both, Q is 1." The reason why XOR might not be included in a list of gates is because you can implement it easily using the original three gates listed. Here is one implementation:

If you try all four different patterns for A and B and trace them through the circuit, you will find that Q behaves like an XOR gate. Since there is a well-understood symbol for XOR...