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DesignerDonald Knuth
Designaccumulator machine
BranchingCondition code and register test
OpenYes, and royalty free
9 in total

MIX is a hypothetical computer used in Donald Knuth's monograph, The Art of Computer Programming (TAOCP). MIX's model number is 1009, which was derived by combining the model numbers and names of several contemporaneous, commercial machines deemed significant by the author. Also, "MIX" read as a Roman numeral is 1009.

The 1960s-era MIX has since been superseded by a new (also hypothetical) computer architecture, MMIX, to be incorporated in forthcoming editions of TAOCP.

Software implementations for both the MIX and MMIX architectures have been developed by Knuth and made freely available (named "MIXware" and "MMIXware", respectively). Several derivatives of Knuth's MIX/MMIX emulators also exist. GNU MDK is one such software package; it is free and runs on a wide variety of platforms.

Their purpose for education is quite similar to John L. Hennessy's and David A. Patterson's DLX architecture, from Computer Organization and Design - The Hardware Software Interface.


MIX is a hybrid binarydecimal 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 −1,073,741,823 to 1,073,741,823 (inclusive) in binary mode, and −9,999,999,999 to 9,999,999,999 (inclusive) in decimal mode. The sign-and-magnitude representation of integers in the MIX architecture distinguishes between “−0” and “+0.” This contrasts with modern computers, whose two's-complement representation of integer quantities includes a single representation for zero, but whose range for a given number of bits includes one more negative integer than the number of representable positive integers.

MIX registers
30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 09 08 07 06 05 04 03 02 01 00 (bit position)
± A1 A2 A3 A4 A5 rA, Accumulator
± X1 X2 X3 X4 X5 rX, Extension
Index registers
  ± I1.4 I1.5 rI1, Index 1
  ± I2.4 I2.5 rI2, Index 2
  ± I3.4 I3.5 rI3, Index 3
  ± I4.4 I4.5 rI4, Index 4
  ± I5.4 I5.5 rI5, Index 5
  ± I6.4 I6.5 rI6, Index 6
Program counter
  J4 J5 rJ, Jump
Condition code flags
  O Overflow flag
  <=> Comparison flag


There are 9 registers in MIX:

  • rA: Accumulator (full word, five bytes and a sign).
  • rX: Extension (full word, five bytes and a sign).
  • rI1, rI2, rI3, rI4, rI5, rI6: Index registers (two bytes and a sign).
  • rJ: Jump address (two bytes, always positive).

A byte is assumed to be at least 6 bits. Most instructions can specify which of the "fields" (bytes) of a register are to be altered, using a suffix of the form (first:last). The zeroth field is the one-bit sign.

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

Memory and input/output[edit]

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).


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 or memory location will be read or altered; and the operation code (1 byte). All operation codes have an associated mnemonic.

30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 09 08 07 06 05 04 03 02 01 00
± Address Index Modification Operation

MIX programs frequently use self-modifying code, in particular to return from a subroutine, as MIX lacks an automatic subroutine return stack. Self-modifying code is facilitated by the modification byte, allowing the program to store data to, for example, the address part of the target instruction, leaving the rest of the instruction unmodified.

MIX programs are typically constructed using the MIXAL assembly language; for an example, see the list hello world programs page.

LDA ADDR,i(0:5) rA := memory[ADDR + rIi];
LDX ADDR,i(0:5) rX := memory[ADDR + rIi];
LD? ADDR,i(0:5) rI? := memory[ADDR + rIi];
LDAN ADDR,i(0:5) rA := - memory[ADDR + rIi];
LDXN ADDR,i(0:5) rX := - memory[ADDR + rIi];
LD?N ADDR,i(0:5) rI? := - memory[ADDR + rIi];
STA ADDR,i(0:5) memory[ADDR + rIi] := rA;
STX ADDR,i(0:5) memory[ADDR + rIi] := rX;
ST? ADDR,i(0:5) memory[ADDR + rIi] := rI?;
STJ ADDR,i(0:5) memory[ADDR + rIi] := rJ;
STZ ADDR,i(0:5) memory[ADDR + rIi] := 0;
ADD ADDR,i(0:5) rA := rA + memory[ADDR + rIi];
SUB ADDR,i(0:5) rA := rA - memory[ADDR + rIi];
MUL ADDR,i(0:5) (rA,rX) := rA * memory[ADDR + rIi];
DIV ADDR,i(0:5)
rA := int( (rA,rX) / memory[ADDR + rIi] );
rX := (rA,rX) % memory[ADDR + rIi];
ENTA ADDR,i rA := ADDR + rIi;
ENTX ADDR,i rX := ADDR + rIi;
ENT? ADDR,i rI? := ADDR + rIi;
ENNA ADDR,i rA := - ADDR - rIi;
ENNX ADDR,i rX := - ADDR - rIi;
ENN? ADDR,i rI? := - ADDR - rIi;
INCA ADDR,i rA := rA + ADDR + rIi;
INCX ADDR,i rX := rX + ADDR + rIi;
INC? ADDR,i rI? := rI? + ADDR + rIi;
DECA ADDR,i rA := rA - ADDR - rIi;
DECX ADDR,i rX := rX - ADDR - rIi;
DEC? ADDR,i rI? := rI? - ADDR - rIi;
CMPA ADDR,i(0:5) compare rA with memory[ADDR + rIi];
CMPX ADDR,i(0:5) compare rX with memory[ADDR + rIi];
CMP? ADDR,i(0:5) compare rI? with memory[ADDR + rIi];
rJ := address of next instruction;
goto ADDR + rIi;
JSJ ADDR,i goto ADDR + rIi;
if (overflow) then
   overflow := false; 
   goto ADDR + rIi;
if (no overflow) then
    goto ADDR + rIi;
    overflow := false;
if (less, equal, greater) then goto ADDR + rIi;
if (no less, unequal, no greater) then goto ADDR + rIi;
if (rA<0 or rA==0 or rA>0) then goto ADDR + rIi;
if (rA>=0 or rA!=0 or rA<=0) then goto ADDR + rIi;
if (rX<0 or rX==0 or rX>0) then goto ADDR + rIi;
if (rX>=0 or rX!=0 or rX<=0) then goto ADDR + rIi;
if (rI?<0 or rI?==0 or rI?>0) then goto ADDR + rIi;
if (rI?>=0 or rI?!=0 or rI?<=0) then goto ADDR + rIi;
for (n = 0; n < F; n++, rI1++)
    memory[rI1] := memory[ADDR+rIi+n];
shift rA to the left/right by ADDR+rIi bytes
shift (rA,rX) to the left/right by ADDR+rIi bytes
rotate (rA,rX) to the left/right by ADDR+rIi bytes
NOP do nothing;
HLT halt execution;
IN ADDR,i(F) read in one block from input unit F
into memory[ADDR + rIi] onwards;
OUT ADDR,i(F) output one block to unit F
from memory[ADDR + rIi] onwards;
IOC ADDR,i(F) send control instruction to i/o unit F;
JRED ADDR,i(F) if (i/o unit F is ready) then goto ADDR + rIi;
JBUS ADDR,i(F) if (i/o unit F is busy) then goto ADDR + rIi;
NUM rA := numerical value of characters in (rA,rX);
CHAR (rA,rX) := character codes representing value of rA;


MIX has been implemented in software by:

An implementation of MIX was created for the iCE40HX8K FPGA board in 2021.[3]

See also[edit]


  1. ^ mix(1) – 9front manual page
  2. ^ Hardware::Simulator::MIX Perl module from CPAN
  3. ^ "Michael Schröder / mix-fgpa". GitLab.

External links[edit]