MIX

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MIX is the mythical computer used in Donald Knuth's textbook trilogy, The Art of Computer Programming. MIX's model number is 1009, which was chosen by combining the model numbers and names of other machines the author was familiar with. (Conveniently, the roman number "MIX" equals 1009.) MIX is planned to be replaced by a wholly new machine, MMIX, in forthcoming editions of TAoCP. In the meantime, you can find software that emulates MIX (called MIXware by Knuth). The GNU MDK is one such software package; it is free, and known to be running on a wide variety of platforms.

Table of contents

1 Architecture 1.1 Registers 1.2 Memory and Input/Output 1.3 Instructions

Architecture

MIX is both a binary and a decimal computer. When programmed in binary, each byte has 6 bits (values range from 0 to 63). In decimal, each byte has 2 decimal digits (values range from 0 to 99). Bytes are grouped into words of five bytes plus a sign. Most programs written for MIX will work in either binary or decimal, so long as they do not try to store a value greater than 63 in a single byte.

A word has the range -1,073,741,824 to 1,073,741,824 (on a binary machine), or -10,000,000,000 to 10,000,000,000 (decimal machine) and distinguishes between +0 and -0. (Most modern machines use two's complement binary arithmetic, and have only one zero. Programming arithmetic on MIX requires taking into account the fact that +0 ≠ -0.)

Registers

There are 9 registers in MIX:

• rA: Accumulator (full word).
• rX: Extension (full word).
• rI1 ... rI6: Index registers (two bytes and a sign).
• rJ: Jump address (two bytes, always positive).

MIX records whether the previous operation overflowed, and a comparison indicator (less than, equal to, or greater than).

Memory and Input/Output

The MIX machine has 4000 words of storage (each with 5 bytes and a sign), addressed from 0 to 3999. A variety of input and output devices are also included:

• Tape units (devices 0 ... 7).
• Disk or drum units (devices 8 ... 15).
• Card reader (device 16).
• Card punch (device 17).
• Line printer (device 18).
• Typewriter terminal (device 19).
• Paper tape (device 20).

Instructions

Each machine instruction in memory occupies one word, and consists of 4 parts: the address (2 bytes and the sign of the word) in memory to read or write; an index specification (1 byte, describing which rI index register to use) to add to the address; a modification (1 byte) that specifies which parts of the register will be read or altered; and the operation code (1 byte). All operation codes have an associated mnemonic.

MIX programs are typically constructed using the MIXAL assembly-like language; for an example, see the page.