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Subsections

Figures

[The manuscript contains a number of figures at the end. Some of these are conversion and arithmetic tables whose details are of no conceivable historical interest; I just briefly describe them on this page. Those containing reference information not available elsewhere are given in on succeeding pages.]

Fig. A -- Powers of 10

[This figure is a table giving powers of 10 in teleprint code, with appropriate scale factors. The last lines are:

$2^{-30}10^{20}$ PSVGZQP@
$2^{105}10^{-20}$ DLN¼¼BBJ
All powers of ten between these two are given.]

Fig. B -- Binary-Decimal Conversion Table

[Conversion table for integers from 0 to 1023, with fractional equivalents alongside for use in interpolation.]

Fig. C -- Multiplication table

Fig. D -- Addition table

[These are two tables for the standard operations in base-32 arithmetic, much like grade-school addition and multiplication tables for decimal arithmetic except with 32 columns and rows.]

Fig. H -- Multiplication by powers of 2

[A table to aid in computing the results of what we'd now call a shift operation, for readers who had not yet memorized the complete list of binary equivalents for teleprint code.]

Fig. E -- Table of function symbols

Function symbol Equations Time in beats
     
// H as mag.instr. ${\tt\bf C}'=\{{\tt\bf C}_++1\}_0^9$ or ${\tt\bf C}'=\{{\tt\bf C}_++3\}_0^9$ Various
/E ${\tt\bf S}' = {\tt\bf M}$ 5
/@ ${\tt\bf A}' = \{ {\tt\bf A}_+ + 2^{40}\mu({\tt\bf S}) \}_0^{79}$ 24
/A ${\tt\bf S}' = {\tt\bf M}$, ${\tt\bf A}'=\{{\tt\bf L}_+\}_0^{79}$ 5
/: $\{{\tt\bf S}_+\}_0^{19}$ as mag.instr. ${\tt\bf C}'$ as for // Various
/S ${\tt\bf S}' = {\tt\bf L}$ 5
/I ${\tt\bf L}' = {\tt\bf M}$, ${\tt\bf M}'={\tt\bf L}$, $({\tt\bf A}'={\tt\bf A}')$ 5
/U ${\tt\bf S}' = {\tt\bf L}$, ${\tt\bf A}'=\{{\tt\bf M}_+\}_0^{79}$ 5
${\tt\bf A}' = \{{\tt\bf A}_+ - {\tt\bf D}{\tt\bf S}_+\}_0^{79}$ 9
/D ${\tt\bf A}' = \{{\tt\bf A}_+ - {\tt\bf D}{\tt\bf S}_\pm\}_0^{79}$ 9
/R ${\tt\bf A}' = \{ {\tt\bf A}_+ + 2^{40}t({\tt\bf S}) \}_0^{79}$ 5 or 7
/J ${\tt\bf A}'=\{{\tt\bf A}_++2^{40}{\tt\bf S}_+\}_0^{79}$ 5
/N ${\tt\bf A}' = \{{\tt\bf A}_+ + {\tt\bf D}{\tt\bf S}_+\}_0^{79}$ 9
/F ${\tt\bf A}' = \{{\tt\bf A}_+ + {\tt\bf D}{\tt\bf S}_\pm\}_0^{79}$ 9
/C ${\tt\bf D}' = {\tt\bf S}_+$ 5
/K ${\tt\bf D}' = {\tt\bf S}_\pm$ 5
/T ${\tt\bf C}'=\{{\tt\bf S}_+ + {\tt\bf Q}({\tt\bf C}_+ + 1-{\tt\bf S}_+)\}_0^9$ 4
/Z $\{{\tt\bf S}_+'\}_0^{19}={\tt\bf H}$, $\{{\tt\bf S}_+'\}_{20}^{39} = \{{\tt\bf S}_+\}_{20}^{39}$ 4
/L Dummy stop 4
/W $\{{\tt\bf A}_+'\}_0^{19}={\tt\bf R}$, $\{{\tt\bf A}_+'\}_{20}^{79} = \{{\tt\bf A}_+\}_{20}^{79}$ 24
/H ${\tt\bf C}'=\{({\tt\bf C}_+ +1)\sigma({\tt\bf A})+
(1-\sigma({\tt\bf A})){\tt\bf S}_+\}_0^9$ 4
/Y $\{{\tt\bf S}_+'\}_0^{19}={\tt\bf Z}$, $\{{\tt\bf S}_+'\}_{20}^{39} = \{{\tt\bf S}_+\}_{20}^{39}$ 4
/P ${\tt\bf C}'=\{{\tt\bf S}_+\}_0^9$ 4
/Q ${\tt\bf C}'=\{{\tt\bf C}_+ + 1 + {\tt\bf S}_+\}_0^9$ 4
/O ${\tt\bf C}'=\{{\tt\bf C}_+ + 1 + {\tt\bf S}_+(1 - {\tt\bf Q})\}_0^9$ 4
/B   4
/G Dummy stop 4
/"   4
/M ${\tt\bf C}'=\{{\tt\bf C}_+ + 1+ {\tt\bf S}_+(1-\sigma({\tt\bf A}))\}_0^9$ 4
/X   4
/V Hoot 4
  4
   
Function symbol B-exc Equations Time in beats
       
T/   ${\tt\bf A}' = \{{\tt\bf S}_+\}_0^{79}$ 5
TE   ${\tt\bf L}'={\tt\bf S}'={\tt\bf S}\lor{\tt\bf L}$, ${\tt\bf M}' = {\tt\bf M}$, ( ${\tt\bf A}'={\tt\bf A}'$) 5
T@   see p. [*] 5
TA   ${\tt\bf S}' = {\tt\bf L}$, ${\tt\bf A}' = \{0\}_0^{79}$ 5
T:   ${\tt\bf A}' = \{0\}_0^{79}$ 5
TS   ${\tt\bf S}' = {\tt\bf L}\lor {\tt\bf S}$, ${\tt\bf A}' = \{0\}_0^{79}$ 5
TI   ${\tt\bf A}' = \{{\tt\bf A}_+ + {\tt\bf S}_+\}_0^{79}$ 5
TU   as TS 5
  ${\tt\bf A}' = \{{\tt\bf S}_\pm\}_0^{79}$ 5
TD   ${\tt\bf A}'={\tt\bf A}'\lor\{{\tt\bf S}_\pm\}_0^{79}$ 5
TR   ${\tt\bf A}'={\tt\bf A}'\land\{{\tt\bf S}_\pm\}_0^{79}$ 5
TJ   ${\tt\bf A}'={\tt\bf A}'\not\equiv \{{\tt\bf S}_\pm\}_0^{79}$ 5
TN   ${\tt\bf A}' = \{{\tt\bf A}_\pm - {\tt\bf S}_\pm\}_0^{79}$ 5
TF   ${\tt\bf A}' = \{- {\tt\bf S}_\pm\}_0^{79}$ 5
TC   ${\tt\bf A}' = \{{\tt\bf A}_\pm + {\tt\bf S}_\pm\}_0^{79}$ 5
TK   ${\tt\bf A}' = \{2{\tt\bf S}_\pm\}_0^{79}$ 5
TT   ${\tt\bf B}'=\{{\tt\bf S}_+\}_0^{19}$, ${\tt\bf Q}' = \sigma({\tt\bf B}')$ 4
TZ   $\{{\tt\bf S}_+'\}_0^{19} = {\tt\bf B}$, $\{{\tt\bf S}_+'\}_{20}^{39} = \{{\tt\bf S}_+\}_{20}^{39}$, ${\tt\bf Q}' = \sigma({\tt\bf B}')$ 4
TL   ${\tt\bf B}'=\{{\tt\bf B}_+-{\tt\bf S}_+\}_0^{19}$, ${\tt\bf Q}' = \sigma({\tt\bf B}')$ 4
TW   as TL 4
TH     4
TY     4
TP     4
TQ     4
TO * as TT 4
TB * as TZ 4
TG * as TL 4
T" * $[$as TL$]$ 4
TM *   4
TX *   4
TV *   4
* Official dummy 4

No B line is added to instructions marked ``B-exc''.
An abbreviated version of this figure is presented in Fig.G.

Definitions  
If ${\tt\bf S}_+ \ne 0$ then $2^{\mu({\tt\bf S})} \le {\tt\bf S}_+ < 2^{\mu({\tt\bf S}) + 1}$  
if ${\tt\bf S}_+ = 0$ then $\mu({\tt\bf S}) = 0$  
$t({\tt\bf S}) = $ number of 1's in S  
R= random digits  
Z= clock  
Normal Equations  
${\tt\bf A}'={\tt\bf A}$ (80 digit), ${\tt\bf C}'=\{{\tt\bf C}_++1\}_0^9$  
${\tt\bf Q}' = {\tt\bf Q}$ (1 digit), ${\tt\bf S}'={\tt\bf S}$ (40 digits)  
${\tt\bf B}' = {\tt\bf B}$ (20 digits), ${\tt\bf D}' = {\tt\bf D}$ (number)  
$[$H= hand switches$]$  
$[{\tt\bf L}= \{{\tt\bf A}\}_0^{39}$, ${\tt\bf M}=\{{\tt\bf A}\}_{40}^{79}]$  

Fig. F -- PERM and the Routine Changing Sequence

\begin{tube}{:}{S}
/ / / / & / & / / / / \\
E / / / & E & / / / @ \\
/ / / / &...
...l}\\
& M & {\rm Working}\\
& X & {\rm Space}\\
& V & \\
& ! &
\end{tube}

The routine changing sequence is entered by the instruction NS/P.

Fig. G -- Summary

[In the manuscript, this is a set of tightly packed and somewhat interleaved tables and lists on two sides of a single sheet of paper, intended as a quick reference. I can't duplicate the formatting in TEX, but the content follows.]



       PERM
    / / / /   /   / / / /
    E / / /   E   / / / @
    / / / /   @   / / / /
    @ / / /   A   / / / :
    / / / /   :   / / / /
    : / / /   S   / / / ¼
    / / / /   I   / / / /
    ¼ / / /   U   / / / /
    / / / /   ¼   / / / /
    T / / /   D   £ £ £ £
    / / / /   R   £ £ £ £
    / E / /   J   / / / /
    / / / /   N   F S / V
    / @ / /   F   K S / P
    / / / /   C   V K T A
    / : / /   K   J S / L
    / / / /   T   
    / ¼ / /   Z   
    / / / /   L   
    / T / /   W   
    / / / /   H   
    / / E /   Y   
    / / / /   P   
    / / @ /   Q   
    / / / /   O   
    / / : /   B   
    / / / /   G   
    / / ¼ /   "   
    / / / /   M   
    / / T /   X    
    / / / /   V   --- -
    / / / E   £   |Cue    
$\textstyle \parbox{2.5 in}{
            \begin{tabular}{ccl}
\multicolumn{3}{...
... Input \\
\tp{B} & Check Output \\
\tp{!} & Official Dummy
\end{tabular}}$
NS/P enters routine changing sequence
KS/P enters hoot
Check numbers are $\{1025([\tp{/E}]_+ - [\tp{/A}]_+)\}_{10}^{19}$

Fig. G (Summary), cont.

Input routine examples
KGA@PQRSTUVW gives $[\tp{GA}]_s'=\tp{PQRS}$, $[\tp{''A}]_s'=\tp{TUVW}$
JPQRSCTUVWJ gives $[\tp{C+}]_s'=\tp{PQRS}$, $[\tp{CD}]_s'=\tp{TUVW}$
JPQRSCTUVWH gives no effect
XGAT/ gives $[\tp{HK}]_++2^{40}[\tp{PK}]_+
=\{[\tp{GA}]_+\}_0^{79}$
"/¼I@SP gives $[\tp{/+}]=\{625\}_0^{39}$
"ACG@£ gives no effect
"ACG@P gives hoot stop
Z enters routine changing sequence
Link is $[\tp{HK}]$
Y enters routine changing sequence
Link returns to INPUT
Q¼PIFFLE Carriage return, line feed,
punches PIFFLE
ENGLISH routine
  Letters. Letter shift printing
    except that @ means Figures
  Figures. Figure shift printing
    except that Y means Letters.
    Z,L,W,£ as magnetic special
    functions

Conventions
(i) Use of PERM
(ii) Link in L.
(iii) Entry by cue.
(iv) /E and /A must be filled in a routine and must not be used as working space.
(v) 5 pages currently available.
(vi) Not more than 8 pages available.
(vii) Instructions in /, E, @, A.
(viii) Mention altered lines except on pages 0 and 1 and lines GK, MK and VK
(ix) Leave B0 clear.
(x) Mention unusual uses of B lines.
(xi) Use higher numbered B lines first.
(xii) Mention changes of B lines other than B7.
(xiii) Tracks 0-15 for permanent routines.
(xiv) Tracks 16-31 for less permanent routines.
(xv) Tracks 32-63 working space -- 32 special working space.
(xvi) Disadvantageous features not used.
(xvii) Use only official properties of routines.

Fig. G (Summary), cont.

\begin{tabular}{cllcll\vert ll\vert l}
\tp{//} & {\tt\bf H} as mag. instr. & \...
...p{/V} & Hoot && \tp{TV} & &&\\
\tp{/!} & && \tp{T!} & Dummy &&\\
\end{tabular}


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Next: About this document ... Up: Alan Turing's Manual for Previous: Appendix The
Robert S. Thau 2000-02-13