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Reputation: 31

How can one byte be more significant than another?

The difference between little endian and big endian was explained to me like this: "In little endian the least significant byte goes into the low address, and in big endian the most significant byte goes into the low address". What exactly makes one byte more significant than the other?

Upvotes: 3

Views: 566

Answers (2)

Matteo Italia
Matteo Italia

Reputation: 126937

In any positional numeric system, each digit has a different weight in creating the overall value of the number.

Consider the number 51354 (in base 10): the first 5 is more significant than the second 5, as it stands for 5 multiplied by 10000, while the second 5 is just 5 multiplied by 10.

In computers number are generally fixed-width: for example, a 16 bit unsigned integer can be thought as a sequence of exactly 16 binary digits, with the leftmost one being unambiguously the most significant (it is worth exactly 32768, more than any other bit in the number), and the rightmost the least significant (it is worth just one).

As long as integers are in the CPU registers we don't really need to care about their representation - the CPU will happily perform operations on them as required. But when they are saved to memory (which generally is some random-access bytes store), they need to be represented as bytes in some way.

If we consider "normal" computers, representing a number (bigger than one byte) as a sequence of bytes means essentially representing it in base 256, each byte being a digit in base 256, and each base-256 digit being more or less significant.

Let's see an example: take the value 54321 as a 16 bit integer. If you write it in base 256, it'll be two base-256 digits: the digit 0xD41 (which is worth 0xD4 multiplied by 256) and the digit 0x31 (which is worth 0x31 multiplied by 1). It's clear that the first one is more significant than the second one, as indeed the leftmost "digit" is worth 256 times more than the one at its right.

Now, little endian machines will write in memory the least significant digit first, big endian ones will do the opposite.

Incidentally, there's a nice relationship between binary, hexadecimal and base-256: 4 bits are mapped straight to a hexadecimal digit, and 2 hexadecimal digits are mapped straight to a byte. For this reason you can also see that 54321 is in binary 

1101010000110001 = 0xD431

can be split straight into two groups of 8 bits

11010100 00110001

which are the 0xD4 and 0x31 above. So you can see as well that the most significant byte is the one that contains the most significant bits.

  1. Here I'm using the corresponding hexadecimal values to represent each base-256 digit, as there's no good way to represent them symbolically. I could use their ASCII character value, but I 0xD4 is outside ASCII, and 0x31 is 1, which would only add confusion.

Upvotes: 1

Andrew Morton
Andrew Morton

Reputation: 25066

In the number 222, you could regard the first 2 as most significant because it represents the value 200; the second 2 is less significant because it represents the value 20; and the third 2 is the least significant digit because it represents the value 2.

So, although the digits are the same, the magnitude of the number they represent is used to determine the significance of a digit.

It is the same as when a value is rounded to a number of significant figures ("S.F." or "SF"): 123.321 to 3SF is 123, to 2SF it is 120, to 4SF it is 123.3. That terminology has been used since before electronics were invented.

Upvotes: 3

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