When the higher-order byte is stored in the lower address, it is sometime referred to as "big endien" (the big end is stored first).  Some machines do store the lower-order byte first, thus 123(b16) stored at loc would be stored 23 in loc and 1 in loc+1.  The representation, known as little endien (the little end stored first) is useful because the first encountered byte in an operational field (address or immediate) following the instruction is always the low-order byte - independent of the size of operand.  (The terms big endien and little endien are a play on words first used in Gulliver's Travels by Jonathan Swift to refer to those who argued that eggs should be broken at the big or little ends.  Does this suggest that some think the argument is silly?)

  Computer Organization: A Top Down Approach by Greg W. Scragg.  
  McGraw-Hill, 1992, Page 170


Digital and Intel are little endien byte ordering, while HP and Sun Sparc use big endien.