Xjyuk

Was there some particular design theory or constraint that made a 36 bit word size attractive for early computers? As opposed to the various power-of-2 word sizes which seem to have won out?

Was there some particular design theory or constraint that made a 36 bit word size attractive for early computers?

Beside integer arithmetic 36 bit words work quite fine with two different byte sizes: Six and nine. Six bit was whats needed to store characters of the standard code for data transmission at that time: Baudot code or more exact ITA2.

As opposed to the various power-of-2 word sizes?

There is no inherent benefit of power of two word sizes. Any number can do.

Even more, there were no 'various power-of-two sizes' in the early and not so early days. Before the IBM/360 settled for a 32 Bit word size and four 8 bit bytes within a word and two nibble in a byte, power-of-two word sizes where an extreme exception (can't come up with any beside SAGE and IBM Stretch). The vast majority used word sizes dividable by 3 not at least to allow the use of octal representation. Before the IBM /360 with its 8 bit bytes, octal was as common to computer scientists as hex today - heck, Unix carries this legacy until today, making everyone learn octal at a time when hex is the general accepted way to display binary data.

Now, the reason why Amdahl did choose 8 bit bytes is rather simple: it was the most efficient way to store two BCD digits within a bye and thus a word as well. Operating in BCD was one main requirement for the /360 design, as it was meant to not only be compatible to, but as well replace all prior decimal machinery.

Is what seams today as 'natural' use of power of two it just a side effect from being able to handle decimal by a binary computer.

Conclusion: As so often in computing the answer is IBM /360 and the rest is history :)

Wiki page 36-bit shows some reasons (all copied from the page):

• "This was long enough to represent positive and negative integers to an accuracy of ten decimal digits (35 bits would have been the minimum). It also allowed the storage of six alphanumeric characters encoded in a six-bit character code. "



• 
  

  And for characters:

  
  
  
  • six 5.32-bit DEC Radix-50 characters, plus four spare bits
  
  
  • six 6-bit Fieldata or IBM BCD characters (ubiquitous in early usage)
  
  
  • six 6-bit ASCII characters, supporting the upper-case unaccented letters, digits, space, and most ASCII punctuation characters. It was used on the PDP-6 and PDP-10 under the name sixbit.
  
  
  • five 7-bit characters and 1 unused bit (the usual PDP-6/10 convention, called five- seven ASCII)1[2]
  
  
  • four 8-bit characters (7-bit ASCII plus 1 spare bit, or 8-bit EBCDIC), plus four spare bits
  
  
  • four 9-bit characters1[2] (the Multics convention).
  
  

36 bit word size attractive

Many sizes have been tried, but fundamentally, this results in a certain precision; from Wikpedia on 36-bit

Early binary computers aimed at the same market therefore often used a 36-bit word length. This was long enough to represent positive and negative integers to an accuracy of ten decimal digits (35 bits would have been the minimum). It also allowed the storage of six alphanumeric characters encoded in a six-bit character code.

As opposed to the various power-of-2 word sizes?

It is lack of requirement to conform to pre-existing specifications, for example, no internet, even simple disc files were not easily shared between computers back in those days.

The key point made by Wikipedia seems to be:

Prior to the introduction of computers, the state of the art in precision scientific and engineering calculation was the ten-digit, electrically powered, mechanical calculator....Computers, as the new competitor, had to match that accuracy....

Many early computers did this by storing decimal digits. But when switching to binary:

Early binary computers aimed at the same market therefore often used a 36-bit word length. This was long enough to represent positive and negative integers to an accuracy of ten decimal digits (35 bits would have been the minimum).

35 bits is obviously a slightly more awkward size than 36 bits anyway, but there are other reasons to choose it if your minimium size is 35 bits.

1. 
   

   36 bits was on average a bit more efficient when packing characters into a word, especially for the 6-bit character encodings common at the time:

   
   
   

   Char size | 35 bit word | 36 bit word
   ----------+-------------------+-------------------
    6-bit | 5 + 5 bits unused | 6 + 0 bits unused
    7-bit | 5 + 0 bits unused | 5 + 1 bit unused
    8-bit | 4 + 3 bits unused | 4 + 4 bits unused
   

   
   



2. If you intend to make smaller computers later, having registers that are exactly divisible by two makes having some level of data interoperability easier, if not perfect. (Numerical data can easily be split into high and low words, and 6-char x 6-bit words can be split into two 3-char words, but packed 7- and 8-bit character data would be splitting parts of characters between words.)