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:

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
`/¼`	${\tt\bf A}' = \{{\tt\bf A}_+ - {\tt\bf D}{\tt\bf S}_+\}_0^{79}$	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
`T¼`		${\tt\bf A}' = \{{\tt\bf S}_\pm\}_0^{79}$	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
`T£`	*	Official dummy	4

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

Fig. F -- PERM and the Routine Changing Sequence

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.

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.

$2^{-30}10^{20}$	`PSVGZQP@`
$2^{105}10^{-20}$	`DLN¼¼BBJ`

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
$[{\tt\bf L}= \{{\tt\bf A}\}_0^{39}$ , ${\tt\bf M}=\{{\tt\bf A}\}_{40}^{79}]$

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