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Resulution of vactors helpful!

vector

Vector Addition: 6 + 8 = ?

Most of us are accustomed to the following form of mathematics:

6 + 8 = 14.

Yet, we are extremely uneasy about this form of mathematics:

6 + 8 = 10

and

6 + 8 = 2

and

6 + 8 = 5.

When we become students of physics and approach the task of adding vector quantities, we soon become aware of the fact that the addition of two vector quantities with magnitudes of 6 and 8 will not necessarily result in an answer of 14. The rules for adding vector quantities are different than the rules for adding two quantities arithmetically. Thus, vectors with magnitudes of 6 + 8 will not necessarily sum to 14.

Vectors are quantities which include a direction. As such, the addition of two or more vectors must take into account that the quantities being added have a directional characteristic. There are a number of methods for carrying out the addition of two (or more) vectors. The most common method is the head-to-tail method of vector addition. Using such a method, the first vector is drawn to scale in the appropriate direction. The second vector is then drawn such that itstail is positioned at the head (vector arrow) of the first vector. The sum of two such vectors is then represented by a third vector which stretches from the tail of the first vector to the head of the second vector. This third vector is known as the resultant - it is the result of adding the two vectors. The resultant is the vector sum of the two individual vectors. Of course, the actual magnitude and direction of the resultant is dependent upon the direction which the two individual vectors have.

This principle of the head-to-tail addition of vectors is illustrated in the animation below. In each frame of the animation, a vector with magnitude of 6 (in green) is added to a vector with magnitude of 8 (in blue). The resultant is depicted by a black vector which stretches from the tail of the first vector (8 units) to the head of the second vector (6 units).

As can be seen from this animation, 8 + 6 could be equal to 14, but only if the two vectors are directed in the same direction. All that can be said for certain is that 8 + 6 can add up to a vector with a maximum magnitude of 14 and a minimum magnitude of 2. The maximum is obtained when the two vectors are directed in the same direction. The minimum s obtained when the two vectors are directed in the opposite direction.

Posted by muneeb:

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Hexadecimal is base 16.
Base 16 is where the 'numbers' you can use are zero through to the letter F (0123456789ABCDEF). i.e. the decimal value for '1' is represented in hexadecimal as '1' but the hexadecimal value of '15' (decimal) is shown as 'F' (hexadecimal) and the value of '17' (decimal) is '11' in Hexadecimal.

Decimal	Hex	Decimal	Hex	Decimal	Hex
1	1	11	B	30	1E
2	2	12	C	40	28
3	3	13	D	50	32
4	4	14	E	60	3C
5	5	15	F	70	46
6	6	16	10	80	50
7	7	17	11	90	5A
8	8	18	12	100	64
9	9	19	13	500	1F4
10	A	20	14	1000	3E8

POSTED BY:
MUNEEB

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Converting Binary to Hexadecimal ...

You need to become VERY familiar with the patterns below:

Hex	F	E	D	C	B	A	9	8	7	6	5	4	3	2	1
Binary	1111	1110	1101	1100	1011	1010	1001	1000	0111	0110	0101	0100	0011	0010	0001
Decimal	15	14	13	12	11	10	9	8	7	6	5	4	3	2	1

There is no easy way to remember the Hex to Binary conversions for A to F. You need to learn them so you can automatically write them down without thinking. Once you have learnt the A to F conversion the process of general conversion from Hex to Binary and back becomes very simple. (So learn them!!)

Binary to Hex

In the previous screens you converted a Hexadecimal number to Binary by expressing each Hex place as a Binary "quartet" (ie 4-bits). The process of converting from Binary to Hex uses the same 'quartet' approach, but in reverse.

Example 1. Consider Binary: 1000100100110111  (a 16-bit Byte)STEP 1 Break the Byte into 'quartets' -  1000  1001  0011  0111 STEP 2 Use the table above to covert each quartet to its Hex equivalent -  8937 Therefore ... 1000100100110111 = 8937Hex

Example 2. Consider Binary 1111110001000001STEP 1 Break the Byte into 'quartets' - 1111  1100  0100 0001 STEP 2 Use the table above to covert each quartet to its Hex equivalent -  FC41 Therefore ... 1111110001000001 = FC41Hex

Example 3. Consider Binary 11010101STEP 1 Break the Byte into 'quartets' - 1101  0101 STEP 2 Use the table above to covert each quartet to its Hex equivalent -  D5 Therefore ... 11010101 = D5Hex Posted by: MUNEEB

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