Editing MIX (abstract machine)

{{Short description|Hypothetical computer by Donald Knuth}}
{{more citations needed|date=August 2012}}
{{Infobox CPU architecture
| name       = MIX
| designer   = [[Donald Knuth]]
| bits       = [[31-bit computing|31-bit]]
| introduced = 1968
| version    =
| design     = [[accumulator machine]]
| type       = hypothetical
| encoding   = Fixed
| branching  = Condition code and register test
| endianness = Big
| extensions =
| open       = Yes, and royalty free
| registers  = 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The 1960s-era MIX has since been superseded by a new (also hypothetical) computer architecture, [[MMIX]], to be incorporated in forthcoming editions of ''TAOCP''.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 software|free]] and runs on a wide variety of platforms.

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

== Architecture ==
MIX is a hybrid [[binary numeral system|binary]]&ndash;[[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 &minus;1,073,741,823 to 1,073,741,823 (inclusive) in binary mode, and &minus;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 “&minus;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.

{| class="infobox" style="font-size:88%;"
|-
|align="center" |''MIX registers''
|-
|
{| style="font-size:88%;"
|- 
| style="width:10px; text-align:left"  | <sup>3</sup><sub>0</sub>
| style="width:10px; text-align:right" | <sup>2</sup><sub>9</sub>
| style="width:10px; text-align:right" | <sup>2</sup><sub>8</sub>
| style="width:10px; text-align:right" | <sup>2</sup><sub>7</sub>
| style="width:10px; text-align:right" | <sup>2</sup><sub>6</sub>
| style="width:10px; text-align:right" | <sup>2</sup><sub>5</sub>
| style="width:10px; text-align:right" | <sup>2</sup><sub>4</sub>
| style="width:10px; text-align:right" | <sup>2</sup><sub>3</sub>
| style="width:10px; text-align:right" | <sup>2</sup><sub>2</sub>
| style="width:10px; text-align:right" | <sup>2</sup><sub>1</sub>
| style="width:10px; text-align:right" | <sup>2</sup><sub>0</sub>
| style="width:10px; text-align:right" | <sup>1</sup><sub>9</sub>
| style="width:10px; text-align:right" | <sup>1</sup><sub>8</sub>
| style="width:10px; text-align:right" | <sup>1</sup><sub>7</sub>
| style="width:10px; text-align:right" | <sup>1</sup><sub>6</sub>
| style="width:10px; text-align:right" | <sup>1</sup><sub>5</sub>
| style="width:10px; text-align:right" | <sup>1</sup><sub>4</sub>
| style="width:10px; text-align:right" | <sup>1</sup><sub>3</sub>
| style="width:10px; text-align:right" | <sup>1</sup><sub>2</sub>
| style="width:10px; text-align:right" | <sup>1</sup><sub>1</sub>
| style="width:10px; text-align:right" | <sup>1</sup><sub>0</sub>
| style="width:10px; text-align:center"| <sup>0</sup><sub>9</sub>
| style="width:10px; text-align:center"| <sup>0</sup><sub>8</sub>
| style="width:10px; text-align:center"| <sup>0</sup><sub>7</sub>
| style="width:10px; text-align:center"| <sup>0</sup><sub>6</sub>
| style="width:10px; text-align:center"| <sup>0</sup><sub>5</sub>
| style="width:10px; text-align:center"| <sup>0</sup><sub>4</sub>
| style="width:10px; text-align:center"| <sup>0</sup><sub>3</sub>
| style="width:10px; text-align:center"| <sup>0</sup><sub>2</sub>
| style="width:10px; text-align:center"| <sup>0</sup><sub>1</sub>
| style="width:10px; text-align:center"| <sup>0</sup><sub>0</sub>
| style="width:auto; background:white; color:black" | ''(bit position)''
|-
|colspan="32" | '''Registers'''
|- style="background:silver;color:black;text-align:center"
| colspan="1"| ±
| colspan="6"| A1
| colspan="6"| A2
| colspan="6"| A3
| colspan="6"| A4
| colspan="6"| A5
| style="text-align:left;background:white" | '''rA''', Accumulator
|- style="background:silver;color:black;text-align:center"
| colspan="1"| ±
| colspan="6"| X1
| colspan="6"| X2
| colspan="6"| X3
| colspan="6"| X4
| colspan="6"| X5
| style="text-align:left;background:white" | '''rX''', Extension
|-
|colspan="32" | '''Index registers'''
|- style="background:silver;color:black;text-align:center"
| style="background:white" colspan="18"| &nbsp;
| colspan="1"| ±
| colspan="6"| I1.4
| colspan="6"| I1.5
| style="text-align:left;background:white" | '''rI1''', Index 1
|- style="background:silver;color:black;text-align:center"
| style="background:white" colspan="18"| &nbsp;
| colspan="1"| ±
| colspan="6"| I2.4
| colspan="6"| I2.5
| style="text-align:left;background:white" | '''rI2''', Index 2
|- style="background:silver;color:black;text-align:center"
| style="background:white" colspan="18"| &nbsp;
| colspan="1"| ±
| colspan="6"| I3.4
| colspan="6"| I3.5
| style="text-align:left;background:white" | '''rI3''', Index 3
|- style="background:silver;color:black;text-align:center"
| style="background:white" colspan="18"| &nbsp;
| colspan="1"| ±
| colspan="6"| I4.4
| colspan="6"| I4.5
| style="text-align:left;background:white" | '''rI4''', Index 4
|- style="background:silver;color:black;text-align:center"
| style="background:white" colspan="18"| &nbsp;
| colspan="1"| ±
| colspan="6"| I5.4
| colspan="6"| I5.5
| style="text-align:left;background:white" | '''rI5''', Index 5
|- style="background:silver;color:black;text-align:center"
| style="background:white" colspan="18"| &nbsp;
| colspan="1"| ±
| colspan="6"| I6.4
| colspan="6"| I6.5
| style="text-align:left;background:white" | '''rI6''', Index 6
|-
|colspan="32" | '''Program counter'''
|- style="background:silver;color:black;text-align:center"
| style="background:white" colspan="19"| &nbsp;
| colspan="6"| J4
| colspan="6"| J5
| style="text-align:left;background:white" | '''rJ''', Jump
|-
|colspan="32" | '''Condition code flags'''
|- style="background:silver;color:black;text-align:center"
| style="background:white" colspan="30"| &nbsp;
| colspan="1"| O
| style="background:white; color:black;"| Overflow flag
|- style="background:silver;color:black;text-align:center"
| style="background:white" colspan="29"| &nbsp;
| colspan="2"| &lt;=&gt; 
| style="background:white; color:black;"| Comparison flag
|}
|}

=== Registers ===
There are 9 [[processor register|registers]] in MIX:
* '''rA''': [[Accumulator (computing)|Accumulator]] (full word, five bytes and a sign).
* '''rX''': Extension (full word, five bytes and a sign).
* '''rI1''', '''rI2''', '''rI3''', '''rI4''', '''rI5''', '''rI6''': [[Index register]]s (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-[[ternary numeral system|trit]] comparison indicator (less than, equal to, or greater than).

=== Memory and input/output ===
The MIX machine has 4000 words of memory (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 or memory location will be read or altered; and the operation code (1 byte). All operation codes have an associated mnemonic.

{|style="text-align:center;margin-left:0.5in"
|style="width:15px;"|<sup>3</sup><sub>0</sub>
|style="width:15px;"|<sup>2</sup><sub>9</sub>
|style="width:15px;"|<sup>2</sup><sub>8</sub>
|style="width:15px;"|<sup>2</sup><sub>7</sub>
|style="width:15px;"|<sup>2</sup><sub>6</sub>
|style="width:15px;"|<sup>2</sup><sub>5</sub>
|style="width:15px;"|<sup>2</sup><sub>4</sub>
|style="width:15px;"|<sup>2</sup><sub>3</sub>
|style="width:15px;"|<sup>2</sup><sub>2</sub>
|style="width:15px;"|<sup>2</sup><sub>1</sub>
|style="width:15px;"|<sup>2</sup><sub>0</sub>
|style="width:15px;"|<sup>1</sup><sub>9</sub>
|style="width:15px;"|<sup>1</sup><sub>8</sub>
|style="width:15px;"|<sup>1</sup><sub>7</sub>
|style="width:15px;"|<sup>1</sup><sub>6</sub>
|style="width:15px;"|<sup>1</sup><sub>5</sub>
|style="width:15px;"|<sup>1</sup><sub>4</sub>
|style="width:15px;"|<sup>1</sup><sub>3</sub>
|style="width:15px;"|<sup>1</sup><sub>2</sub>
|style="width:15px;"|<sup>1</sup><sub>1</sub>
|style="width:15px;"|<sup>1</sup><sub>0</sub>
|style="width:15px;"|<sup>0</sup><sub>9</sub>
|style="width:15px;"|<sup>0</sup><sub>8</sub>
|style="width:15px;"|<sup>0</sup><sub>7</sub>
|style="width:15px;"|<sup>0</sup><sub>6</sub>
|style="width:15px;"|<sup>0</sup><sub>5</sub>
|style="width:15px;"|<sup>0</sup><sub>4</sub>
|style="width:15px;"|<sup>0</sup><sub>3</sub>
|style="width:15px;"|<sup>0</sup><sub>2</sub>
|style="width:15px;"|<sup>0</sup><sub>1</sub>
|style="width:15px;"|<sup>0</sup><sub>0</sub>
|-
|colspan="1"  style="background-color:#CCC"| ±
|colspan="12" style="background-color:#CCC"| Address
|colspan="6"  style="background-color:#CCF"| Index
|colspan="6"  style="background-color:#CEC"| Modification
|colspan="6"  style="background-color:#FCC"| 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 [[Wikibooks:List of hello world programs#General-purpose fictional computer: MIX.2C MIXAL|list hello world programs]] page.

{| class="wikitable"
|-
! {{rh|align=right}} | {{code|2=asm|LDA ADDR,i(0:5)}}
| {{code|2=pascal|1=rA := memory[ADDR + rIi];}}
|-
! {{rh|align=right}} | {{code|2=asm|LDX ADDR,i(0:5)}}
| {{code|2=pascal|1=rX := memory[ADDR + rIi];}}
|-
! {{rh|align=right}} | {{code|LD? ADDR,i(0:5)}}
| {{code|1=rI? := memory[ADDR + rIi];}}
|-
! {{rh|align=right}} | {{code|2=asm|LDAN ADDR,i(0:5)}}
| {{code|2=pascal|1=rA := - memory[ADDR + rIi];}}
|-
! {{rh|align=right}} | {{code|2=asm|LDXN ADDR,i(0:5)}}
| {{code|2=pascal|1=rX := - memory[ADDR + rIi];}}
|-
! {{rh|align=right}} | {{code|LD?N ADDR,i(0:5)}}
| {{code|1=rI? := - memory[ADDR + rIi];}}
|-
! {{rh|align=right}} | {{code|2=asm|STA ADDR,i(0:5)}}
| {{code|2=pascal|1=memory[ADDR + rIi] := rA;}}
|-
! {{rh|align=right}} | {{code|2=asm|STX ADDR,i(0:5)}}
| {{code|2=pascal|1=memory[ADDR + rIi] := rX;}}
|-
! {{rh|align=right}} | {{code|ST? ADDR,i(0:5)}}
| {{code|1=memory[ADDR + rIi] := rI?;}}
|-
! {{rh|align=right}} | {{code|2=asm|STJ ADDR,i(0:5)}}
| {{code|2=pascal|1=memory[ADDR + rIi] := rJ;}}
|-
! {{rh|align=right}} | {{code|2=asm|STZ ADDR,i(0:5)}}
| {{code|2=pascal|1=memory[ADDR + rIi] := 0;}}
|-
! {{rh|align=right}} | {{code|2=asm|ADD ADDR,i(0:5)}}
| {{code|2=pascal|1=rA := rA + memory[ADDR + rIi];}}
|-
! {{rh|align=right}} | {{code|2=asm|SUB ADDR,i(0:5)}}
| {{code|2=pascal|1=rA := rA - memory[ADDR + rIi];}}
|-
! {{rh|align=right}} | {{code|2=asm|MUL ADDR,i(0:5)}}
| {{code|2=pascal|1=(rA,rX) := rA * memory[ADDR + rIi];}}
|-
! {{rh|align=right}} | {{code|2=asm|DIV ADDR,i(0:5)}}
| {{sxhl|2=c|1=rA := int( (rA,rX) / memory[ADDR + rIi] );
rX := (rA,rX) % memory[ADDR + rIi];}}
|-
! {{rh|align=right}} | {{code|2=asm|ENTA ADDR,i}}
| {{code|2=pascal|1=rA := ADDR + rIi;}}
|-
! {{rh|align=right}} | {{code|2=asm|ENTX ADDR,i}}
| {{code|2=pascal|1=rX := ADDR + rIi;}}
|-
! {{rh|align=right}} | {{code|ENT? ADDR,i}}
| {{code|1=rI? := ADDR + rIi;}}
|-
! {{rh|align=right}} | {{code|2=asm|ENNA ADDR,i}}
| {{code|2=pascal|1=rA := - ADDR - rIi;}}
|-
! {{rh|align=right}} | {{code|2=asm|ENNX ADDR,i}}
| {{code|2=pascal|1=rX := - ADDR - rIi;}}
|-
! {{rh|align=right}} | {{code|ENN? ADDR,i}}
| {{code|1=rI? := - ADDR - rIi;}}
|-
! {{rh|align=right}} | {{code|2=asm|INCA ADDR,i}}
| {{code|2=pascal|1=rA := rA + ADDR + rIi;}}
|-
! {{rh|align=right}} | {{code|2=asm|INCX ADDR,i}}
| {{code|2=pascal|1=rX := rX + ADDR + rIi;}}
|-
! {{rh|align=right}} | {{code|INC? ADDR,i}}
| {{code|1=rI? := rI? + ADDR + rIi;}}
|-
! {{rh|align=right}} | {{code|2=asm|DECA ADDR,i}}
| {{code|2=pascal|1=rA := rA - ADDR - rIi;}}
|-
! {{rh|align=right}} | {{code|2=asm|DECX ADDR,i}}
| {{code|2=pascal|1=rX := rX - ADDR - rIi;}}
|-
! {{rh|align=right}} | {{code|DEC? ADDR,i}}
| {{code|1=rI? := rI? - ADDR - rIi;}}
|-
! {{rh|align=right}} | {{code|2=asm|CMPA ADDR,i(0:5)}}
| compare {{code|rA}} with {{code|memory[ADDR + rIi] and set comparison flag;}}
|-
! {{rh|align=right}} | {{code|2=asm|CMPX ADDR,i(0:5)}}
| compare {{code|rX}} with {{code|memory[ADDR + rIi] and set comparison flag;}}
|-
! {{rh|align=right}} | {{code|CMP? ADDR,i(0:5)}}
| compare {{code|rI?}} with {{code|memory[ADDR + rIi] and set comparison flag;}}
|-
! {{rh|align=right}} | {{code|2=asm|JMP ADDR,i}}
| {{sxhl|2=pascal|1=rJ := address of next instruction;
goto ADDR + rIi;}}
|-
! {{rh|align=right}} | {{code|2=asm|JSJ ADDR,i}}
| {{code|2=pascal|1=goto ADDR + rIi;}}
|-
! {{rh|align=right}} | {{code|2=asm|JOV ADDR,i}}
| {{sxhl|2=pascal|1=
if (overflow) then
   overflow := false; 
   goto ADDR + rIi;}}
|-
! {{rh|align=right}} | {{code|2=asm|JNOV ADDR,i}}
| {{sxhl|2=pascal|1=
if (no overflow) then
    goto ADDR + rIi;
else 
    overflow := false;}}
|-
! {{rh|align=right}} | {{code|JL, JE, JG ADDR,i}}<br>{{code|JGE, JNE, JLE ADDR,i}}
| {{sxhl|2=pascal|1=if (less, equal, greater) then goto ADDR + rIi;
if (no less, unequal, no greater) then goto ADDR + rIi;}}
|-
! {{rh|align=right}} | {{code|JAN/JAZ/JAP ADDR,i}}<br>{{code|JANN/JANZ/JANP ADDR,i}}
| {{sxhl|2=pascal|1=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;}}
|-
! {{rh|align=right}} | {{code|JXN/JXZ/JXP ADDR,i}}<br>{{code|JXNN/JXNZ/JXNP ADDR,i}}
| {{sxhl|2=text|1=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;}}
|-
! {{rh|align=right}} | {{code|J?N/J?Z/J?P ADDR,i}}<br>{{code|J?NN/J?NZ/J?NP ADDR,i}}
| {{pre|1=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;}}
|-
! {{rh|align=right}} | {{code|2=asm|MOVE ADDR,i(F)}}
| {{sxhl|2=c|1=
for (n = 0; n < F; n++, rI1++)
    memory[rI1] := memory[ADDR+rIi+n];}}
|-
! {{rh|align=right}} | {{code|SLA/SRA ADDR,i}}<br>{{code|SLAX/SRAX ADDR,i}}<br>{{code|SLC/SRC ADDR,i}}
| shift {{code|rA}} to the left/right by {{code|ADDR+rIi}} bytes<br>shift {{code|(rA,rX)}} to the left/right by {{code|ADDR+rIi}} bytes<br>rotate {{code|(rA,rX)}} to the left/right by {{code|ADDR+rIi}} bytes
|-
! {{rh|align=right}} | {{code|NOP}}
| do nothing;
|-
! {{rh|align=right}} | {{code|HLT}}
| halt execution;
|-
! {{rh|align=right}} | {{code|2=asm|IN ADDR,i(F)}}
| read in one block from input unit {{code|F}}<br>into {{code|memory[ADDR + rIi]}} onwards;
|-
! {{rh|align=right}} | {{code|2=asm|OUT ADDR,i(F)}}
| output one block to unit {{code|F}}<br>from {{code|memory[ADDR + rIi]}} onwards;
|-
! {{rh|align=right}} | {{code|2=asm|IOC ADDR,i(F)}}
| send control instruction to i/o unit {{code|F}};
|-
! {{rh|align=right}} | {{code|2=asm|JRED ADDR,i(F)}}
| {{code|2=pascal|1=if (i/o unit F is ready) then goto ADDR + rIi;}}
|-
! {{rh|align=right}} | {{code|2=asm|JBUS ADDR,i(F)}}
| {{code|2=pascal|1=if (i/o unit F is busy) then goto ADDR + rIi;}}
|-
! {{rh|align=right}} | {{code|NUM}}
| {{code|1=rA := numerical value of characters in (rA,rX);}}
|-
! {{rh|align=right}} | {{code|CHAR}}
| {{code|1=(rA,rX) := character codes representing value of rA;}}
|}

== Implementations ==
MIX has been implemented in software by:
* Knuth's ''MIXWare'' and the derived  [[GNU MDK]];
* [[9front]]'s mix(1);<ref>{{man|1|mix|9front}}</ref> and
* Hardware::Simulator::MIX on [[CPAN]].<ref>[https://metacpan.org/module/Hardware::Simulator::MIX Hardware::Simulator::MIX] [[Perl]] module from [[CPAN]]</ref>

An implementation of MIX was created for the iCE40HX8K [[FPGA]] board in 2021.<ref>{{cite web |title=Michael Schröder / mix-fgpa |url=https://gitlab.com/x653/mix-fpga |website=GitLab |language=en}}</ref>

== See also ==
* [[Educational programming language]]
* [[DLX]]
* [[Little Computer 3|LC-3]]
* [[Little man computer]]
* [[MMIX]]
* [[MikroSim]]

== References ==
{{reflist}}

== External links ==
*[https://www-cs-faculty.stanford.edu/~knuth/mmix.html MMIX 2009: A RISC Computer for the Third Millennium] Knuth's official MIX page
*[https://www-cs-faculty.stanford.edu/~knuth/mmix-news.html MMIX News] Knuth's official MIX news
*{{OL book|id=OL20293437M|cname=MIX: the design of a typical computer and its assembly language}}, Knuth's original 1970 official MIX book, with [[Tom Mix]] on the cover.
*[https://www-cs-faculty.stanford.edu/~knuth/mmixware.html MMIXware: A RISC Computer for the Third Millennium] Knuth's official MIX book

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