Types of endianness

Question

What is the difference between the following types of endianness?

• byte (8b) invariant big and little endianness
• half-word (16b) invariant big and litt

Answer 1

There are two approaches to endian mapping: address invariance and data invariance.

Address Invariance

In this type of mapping, the address of bytes is always preserved between big and little. This has the side effect of reversing the order of significance (most significant to least significant) of a particular datum (e.g. 2 or 4 byte word) and therefore the interpretation of data. Specifically, in little-endian, the interpretation of data is least-significant to most-significant bytes whilst in big-endian, the interpretation is most-significant to least-significant. In both cases, the set of bytes accessed remains the same.

Example

Address invariance (also known as byte invariance): the byte address is constant but byte significance is reversed.

Addr   Memory
       7    0
       |    |    (LE)   (BE)
       |----|
 +0    | aa |    lsb    msb
       |----|
 +1    | bb |     :      :
       |----|
 +2    | cc |     :      :
       |----|
 +3    | dd |    msb    lsb
       |----|
       |    |

At Addr=0:          Little-endian          Big-endian
Read 1 byte:              0xaa                0xaa   (preserved)
Read 2 bytes:           0xbbaa              0xaabb
Read 4 bytes:       0xddccbbaa          0xaabbccdd

Data Invariance

In this type of mapping, the relative byte significance is preserved for datum of a particular size. There are therefore different types of data invariant endian mappings for different datum sizes. For example, a 32-bit word invariant endian mapping would be used for a datum size of 32. The effect of preserving the value of particular sized datum, is that the byte addresses of bytes within the datum are reversed between big and little endian mappings.

Example

32-bit data invariance (also known as word invariance): The datum is a 32-bit word which always has the value 0xddccbbaa, independent of endianness. However, for accesses smaller than a word, the address of the bytes are reversed between big and little endian mappings.

Addr                Memory

            | +3   +2   +1   +0 |  <- LE
            |-------------------|
+0      msb | dd | cc | bb | aa |  lsb
            |-------------------|
+4      msb | 99 | 88 | 77 | 66 |  lsb
            |-------------------|
     BE ->  | +0   +1   +2   +3 |


At Addr=0:             Little-endian              Big-endian
Read 1 byte:                 0xaa                    0xdd
Read 2 bytes:              0xbbaa                  0xddcc
Read 4 bytes:          0xddccbbaa              0xddccbbaa   (preserved)
Read 8 bytes:  0x99887766ddccbbaa      0x99887766ddccbbaa   (preserved)

Example

16-bit data invariance (also known as half-word invariance): The datum is a 16-bit which always has the value 0xbbaa, independent of endianness. However, for accesses smaller than a half-word, the address of the bytes are reversed between big and little endian mappings.

Addr           Memory

            | +1   +0 |  <- LE
            |---------|
+0      msb | bb | aa |  lsb
            |---------|
+2      msb | dd | cc |  lsb
            |---------|
+4      msb | 77 | 66 |  lsb
            |---------|
+6      msb | 99 | 88 |  lsb
            |---------|
     BE ->  | +0   +1 |


At Addr=0:             Little-endian              Big-endian
Read 1 byte:                 0xaa                    0xbb
Read 2 bytes:              0xbbaa                  0xbbaa   (preserved)
Read 4 bytes:          0xddccbbaa              0xddccbbaa   (preserved)
Read 8 bytes:  0x99887766ddccbbaa      0x99887766ddccbbaa   (preserved)

Example

64-bit data invariance (also known as double-word invariance): The datum is a 64-bit word which always has the value 0x99887766ddccbbaa, independent of endianness. However, for accesses smaller than a double-word, the address of the bytes are reversed between big and little endian mappings.

Addr                         Memory

            | +7   +6   +5   +4   +3   +2   +1   +0 |  <- LE
            |---------------------------------------|
+0      msb | 99 | 88 | 77 | 66 | dd | cc | bb | aa |  lsb
            |---------------------------------------|
     BE ->  | +0   +1   +2   +3   +4   +5   +6   +7 |


At Addr=0:             Little-endian              Big-endian
Read 1 byte:                 0xaa                    0x99
Read 2 bytes:              0xbbaa                  0x9988
Read 4 bytes:          0xddccbbaa              0x99887766
Read 8 bytes:  0x99887766ddccbbaa      0x99887766ddccbbaa   (preserved)

Answer 2

Best article I read about endianness "Understanding Big and Little Endian Byte Order".