Suppose a₁a₂a₃a₄ are the 4 bytes in a 32-bit word. Each a_i can be viewed as an integer in the range 0 to 255, represented in binary. In a big-endian architecture, this word represents the integer

In a little-endian architecture, this word represents the integer

a. Some hash functions, such as MD5, assume a little-endian architecture. It is important that the message digest be independent of the underlying architecture. Therefore, to perform the modulo 2 addition operation of MD5 or RIPEMD-160 on a big-endian architecture, an adjustment must be made. Suppose X = x₁x₂x₃x₄ and Y = y₁y₂y₃y₄. Show how the MD5 addition operation (X + Y) would be carried out on a big-endian machine.

b. SHA assumes a big-endian architecture. Show how the operation (X + Y) for SHA would be carried out on a little-endian machine.

a224 + a226 + a328 + a4