31-bit computing

how 31/32 bit applies to networking and 31 bit subnet masks

In computer architecture, 31 bit integers, memory addresses, or other data units are those that are 31 bits wide. In 1983, IBM introduced 31 bit addressing in the System/370 XA mainframe architecture as an upgrade to the 24 bit physical and virtual, and transitional 24 bit virtual/26 bit physical, addressing in System/370. This enhancement allowed address spaces to be 128 times larger, permitting programs to address memory above 16 MB (referred to as "above the line").

The Librascope LGP 30 was an early off the shelf computer. The LGP 30 was first manufactured in 1956, at a retail price of $47,000, 47000.0 in 1956 is equivalent to about <calculated amount> in recent years. It was a binary, 31 bit word computer with a 4096 word drum memory. There were 32 bit locations per drum word, but only 31 were used, permitting a "restoration of magnetic flux in the head" at the 32nd bit time. The number of vacuum tubes was minimized by using solid state diode logic, a bit serial architecture and multiple use of each of its 15 flip flops. The LGP 30 was commonly referred to as a desk computer. Its height, width, and depth, excluding the typewriter shelf, was 33 by 44 by 26 inches (84 by 112 by 66 cm). It weighed about 800 pounds (360 kg), and was mounted on sturdy casters which facilitated moving the unit.

In the System/360, other than the 360/67, and early System/370 architectures, the general purpose registers were 32 bits wide, the machine did 32 bit arithmetic operations, and addresses were always stored in 32 bit words, so the architecture was considered 32 bit, but the machines ignored the top 8 bits of the address resulting in 24 bit addressing. With the System/370 XA architecture and the IBM Enterprise Systems Architecture, in addition to a 24 bit addressing mode for compatibility with older applications, there is a 31 bit addressing mode, in which only the high order bit (bit 0) in the word is ignored for addressing. An exception is that mode switching instructions also use bit 0. There were at least two reasons that IBM did not implement the 32 bit addressing of the 360/67
The loop control instructions BXH and BXLE did signed comparisons. Much of the existing software used bit 0 as an end of list indicator. The 64 bit z/Architecture also supports 24 bit and 31 bit addressing modes for compatibility with older applications.

Interpreters for Ruby & Smalltalk languages use the lowest bit to tell whether a value is an unboxed integer or not. This means that on 32 bit machines (or 16 bit machines with 32 bit pointers), 31 bit integers are unboxed. In case of overflow, the result is fit into a boxed object, which means that it has to be allocated and garbage collected. Thus if you have 32 bit values that don't fit in the 31 bit signed format, they will be very inefficient in those interpreters. Same goes with 63 bit unboxed integers on 64 bit computers. Similar designs may be found in LISP and some of the other languages whose variables can take values of any type. In some cases, there was hardware support for this kind of design: see Tagged architecture and Lisp machine.