An Essay on Endian Order

Copyright (C) Dr. William T. Verts, April 19, 1996

Depending on which computing system you use, you will have to consider the byte order in which multibyte numbers are stored, particularly when you are writing those numbers to a file. The two orders are called "Little Endian" and "Big Endian".

The Basics

"Little Endian" means that the low-order byte of the number is stored in memory at the lowest address, and the high-order byte at the highest address. (The little end comes first.) For example, a 4 byte LongInt

    Byte3 Byte2 Byte1 Byte0
will be arranged in memory as follows:
    Base Address+0   Byte0
    Base Address+1   Byte1
    Base Address+2   Byte2
    Base Address+3   Byte3
Intel processors (those used in PC's) use "Little Endian" byte order.

"Big Endian" means that the high-order byte of the number is stored in memory at the lowest address, and the low-order byte at the highest address. (The big end comes first.) Our LongInt, would then be stored as:

    Base Address+0   Byte3
    Base Address+1   Byte2
    Base Address+2   Byte1
    Base Address+3   Byte0
Motorola processors (those used in Mac's) use "Big Endian" byte order.

Which is Better?

You may see a lot of discussion about the relative merits of the two formats, mostly religious arguments based on the relative merits of the PC versus the Mac. Both formats have their advantages and disadvantages.

In "Little Endian" form, assembly language instructions for picking up a 1, 2, 4, or longer byte number proceed in exactly the same way for all formats: first pick up the lowest order byte at offset 0. Also, because of the 1:1 relationship between address offset and byte number (offset 0 is byte 0), multiple precision math routines are correspondingly easy to write.

In "Big Endian" form, by having the high-order byte come first, you can always test whether the number is positive or negative by looking at the byte at offset zero. You don't have to know how long the number is, nor do you have to skip over any bytes to find the byte containing the sign information. The numbers are also stored in the order in which they are printed out, so binary to decimal routines are particularly efficient.

What does that Mean for Us?

What endian order means is that any time numbers are written to a file, you have to know how the file is supposed to be constructed. If you write out a graphics file (such as a .BMP file) on a machine with "Big Endian" integers, you must first reverse the byte order, or a "standard" program to read your file won't work.

The Windows .BMP format, since it was developed on a "Little Endian" architecture, insists on the "Little Endian" format. You must write your Save_BMP code this way, regardless of the platform you are using.

Common file formats and their endian order are as follows:

Correcting for the Non-Native Order

It is pretty easy to reverse a multibyte integer if you find you need the other format. A single function can be used to switch from one to the other, in either direction. A simple and not very efficient version might look as follows: Function Reverse (N:LongInt) : LongInt ; Var B0, B1, B2, B3 : Byte ; Begin B0 := N Mod 256 ; N := N Div 256 ; B1 := N Mod 256 ; N := N Div 256 ; B2 := N Mod 256 ; N := N Div 256 ; B3 := N Mod 256 ; Reverse := (((B0 * 256 + B1) * 256 + B2) * 256 + B3) ; End ; A more efficient version that depends on the presence of hexadecimal numbers, bit masking operators AND, OR, and NOT, and shift operators SHL and SHR might look as follows: Function Reverse (N:LongInt) : LongInt ; Var B0, B1, B2, B3 : Byte ; Begin B0 := (N AND $000000FF) SHR 0 ; B1 := (N AND $0000FF00) SHR 8 ; B2 := (N AND $00FF0000) SHR 16 ; B3 := (N AND $FF000000) SHR 24 ; Reverse := (B0 SHL 24) OR (B1 SHL 16) OR (B2 SHL 8) OR (B3 SHL 0) ; End ; There are certainly more efficient methods, some of which are quite machine and platform dependent. Use what works best.

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