2,4,8,16,32,64,128,256,512.. Fibonacci sequences and confusion. can anyone explain? ?

Question

the sequence as above are the steps that computer ram, memory cards etc go up in, can anyone explain mathematically why, and is this a Fibonacci sequence, i thought they were the last two numbers added rather than the last number added to itself.

Answer 1

This is not the Fibonacci sequence. These are integral powers of two starting with the first power.



The reason that these are used (as memory denominations) is because computer systems are based on the binary system. Binary system is based on the number two. The system that we normally use for counting is based on the number ten. So this is how you would count in binary



0

1

10

11

100

101

110

111

1000

1001

1010

1011

1100

1101

1110

1111

10000

and so on.



So number that start with one and are all zeros in binary, are all powers of two, for example



1=1=2^0

10=2=2^1

100=4=2^2

1000=8=2^3

10000=16=2^4

100000=32=2^5

1000000=64=2^6

and so on.



The number on the left (like 1000) is in binary and the number on the right (like 2^3=8) is in decimal which is what we use to count. So RAM modules are made in powers of twos because they are easier to keep track of but general public doesn't know how to count in binary so then the manufacturer's have to translate the numbers into decimal. I mean 1000000 sounds like a lot but it is only 64. So if you tell someone that I am selling your a RAM module with 1000000 bytes and it is actually only 64, we can just see a lawsuit coming up. Both people will be correct but one will be in binary and the other will be in decimal.



And by the way, the list I gave you up above, you count the number of zeros, and then raise 2 to the power of that number.



In addition, this sequence is a geometric sequence.

Answer 2

Nope, it's not a Fibonacci series. It's a binary series, where the nth value is 2^n. All computer arithmetic is binary, so it was a convenience just to double things.



In the Fibonacci sequence of numbers, each number after the first two is the sum of the previous two numbers. Thus the sequence is 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, etc.

Answer 3

hi friend. its very simple

2,4,8,16,32,64,126,256,512,.....



its like 2^1, 2^2, 2^3, 2^4, 2^4,2^5, 2^6......2^n

2^1=2, 2^2=4, 2^3=2*2*2=8 etc.....



i am ready to help you as much as i can

good luck

Answer 4

no your equation basically just doubles itself e.g. 2+2=4, 4+4=8 whereas Fibonacci is the first number of the sequence is 0, the second number is 1, and each subsequent number is equal to the sum of the previous two numbers of the sequence itself.



1 1 2 3 5 8 13 21



1+1=2, 1+2=3, 2+3=5



electronic computers are all based on a binary system.

An electronic switch has only two positions on or off this corresponds

to the number zero or one.

If you have two electronic switches then you can get numbers up to three

or four if you count zero.

Three switches gives you eight.

Four switches gives you 16.

And so on.

2,4,8,16,32,64,128,256,512,1024

and thus for the memory it is just a bunch of switches which can be

used to represent those numbers. The more switches the bigger the number.







The number sequence is 1, 2, 4, 8, 16, 32 etc. The exponential growth of splitting cells. The power of 2s. The heavy silver bauble is like a splitting ovum, that first moment of conception. A fusion of a scientific approach to fertility and something more intuitive, like a sympathetic magic for our time.



also when we say 1gb it is NOT 1000mb in fact it is 1024mb basically your equation is also in which mb and gb work.

Answer 5

This is a geometric sequence. As you can see, each term is a multiple of the one before. In this case the terms double in magnitude. The reason for this involves binary representation of numbers. Computer memory is accessed by using "addresses", which are numbers that indicate locations in memory. Because computers use binary arithmetic, the number of addressable memory locations will always be a power of two.



You're right about Fibonacci sequences. They're distinct from geometric sequences like the one you asked about.



Edit: Other people are calling this a "linear" or "arithmetic" progression. It isn't. In an arithmetic progression, the terms increase *additively*, not multiplicatively like this one. Progressions like



1, 3, 5, 7, 9, 11...



are arithmetic. This one is geometric.

Answer 6

It's the decimal version of a binary arithmetic progression.

Answer 7

The sequence is a simple linear sequenced that can be expressed by 2^x (2 to the x power) where x represents the space in the sequence. ie 1st space (2) equals 2^1 = 2 second space 2^2 =4. It is not a Fibonacci sequence which are the last 2 digits added together to make the next



1,1,2,3,5,8,13,21 etc

Answer 8

This is not the Fibonacci series which is 1 1 2 3 5 8 13 like you said where the last two numbers added together get the next number in the sequence.





2,4,8,16 etc is binary i.e. 2^0 = 1, 2^1 = 2, 2^2 = 4, 2^3 = 8 etc



Binary is used for computers because it means that all numbers can be expressed using just 0s and 1s for example 10 is 2+8 so 0(2^0) + 1(2^1)+0(2^2)+ 1(2^3) --> 10 = 0101 in binary.



This is useful because if you imagine a switch in a computer it can only have two settings on and off which correspond to 1 and 0 in binary.





Hope that helps!

Answer 9

dunno ask someone older