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What is the significance of the power of 2s in computer science and mathematics?
The power of 2s is significant in computer science and mathematics because it is the basis for binary numbering systems, which are fundamental in digital computing. Powers of 2 are used in memory allocation, data storage, and calculations in computer programming. They also play a key role in algorithms, data structures, and other mathematical concepts, making them essential in various computational tasks.
How many IP addresses in one ip octet?
A complete IP address has 4 octets. MPGMichael We are talking IPv4 because IPv6 uses quintets. There are 4 octets in an IPv4 address. Each octet is separated by a dot (.) Each place has a binary value assigned to it as follows. 128s, 64s, 32s, 16s, 8s, 4, 2s, and 1s place The place values repeat in each octet The place values are read from right to left in binary numbers Within each octet there are 2^8 or 2 to the 8thpower possible addresses. So the math answer is 256. However if you write it out you will see that 128+64+32+16+8+4+2+1 = 255 and 256 is actually carried to the next octet. So there are 255 possible addresses in each octet For example a class C address would look like this 192.168.1.2 or binary 11000000.10101000.00000001.00000010
Why do computers use 2s not 10s?
Computers are only capable of differentiating between two possible states. That is: a switch is either on or off; a capacitor is either full of charge or it is empty; a score upon an optical disc is either long or short; there is either a flux transition or there is not; there is either a hole punched at a position on a card or there is not. All are valid ways of representing binary values and all are or have been used by computers at one time or another. We use 1s and 0s, but computers cannot; they are simple machines, they have no actual intelligence whatsoever. They have to use mechanic representations.
How many binary digits has an ip address?
There are 32 binary digits in an IPv4 address. There are 128 binary digits in an IPv6 address IPv4 addresses are organized into four 8 bit octets 11111111. 11111111. 11111111. 11111111 each place can represent either a zero or a one. Each place has an assigned binary place value. 1s, 2s, 4s, 8s, 16, 32s, 64, and 128s place right to left and repeating in each octet. There are 2^32 possible IP addresses = 4,294,967,296 possible addresses; or 4 billion 294 million 967 thousand 296. And they are all used up at this time. IPv4 addresses can also be written in decimal form. If you add all the place values in a single octet (128+64-32+16+8+4+2+1) it will equal decimal 255. IPv4 in decimal, as you will see it everywhere except class will look like this 255.255.255.255 Enough on IPv4 There are 128 binary digits in an IPv6 address. Therefore, there are 2^128 possible IPv6 addresses. That is in English is 340 undecillion, 282 decillion, 366 nonillion, 920 octillion, 938 septillion, 463 sextillion, 463 quintillion, 374 quadrillion, 607 trillion, 431 billion, 768 million, 211 thousand and 456 give or take a few. IPv6 addresses are represented by eight groups of hexadecimal quartets (four of them) separated by colons. Here is an example of a valid IPv6 address: 2001:cdba:0000:0000:0000:0000:3257:9652 Any four-digit group of zeroes within an IPv6 address may be reduced to a single zero or completely omitted. Consequently, the following IPv6 addresses are alike and equally valid. 2001:cdba:0000:0000:0000:0000:3257:9652 2001:cdba:0:0:0:0:3257:9652 2001:cdba::3257:9652 the omitted zeros have to occur together 2001:cdba…..can be converted to binary or decimal. Note each hex value in each quartet represents 4 binary digits. Just examining the second quartet in the above address we have Hex c d b a bin 1100 .1101 .1011 .1010 Dec 12 13 11 10
