[COFF] Make your own virtual punchcard

[COFF] Make your own virtual punchcard

[Douglas McIlroy]

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Mention of punched cards reminded me of some 1960s trivia.

There were two formats for binary code on punched cards for IBM 700-series
machines. In "row binary" two 36-bit words filled each of the 12 rows from
bottom to top. In "column binary" successive thirds of a word ran downward
in each of 3 successive columns. Bob Morris wondered what is the order of
the permutation performed in row-to-column conversion.

The order of the row-to-column permutation turns out to be 172. There are
five cycles of that length plus an oddball  of length 4. My souvenir card
shows the oddball.

If you convert a cycle from row binary to column binary, the output is the
same as the input.* Each cycle is also invariant under 180-degree
rotation.The 4-cycle is a simple parallelogram. One of the 5-cycles lines
up in periodic diagonals. The other cycles show no easily described
structure.

The images of the two described cycles should be viewed in a fixed-width
font. The punches in the 4-cycle are numbered in cyclic order.

I keep a few souvenir punched cards. One bears that 4-cycle.

* Well, almost the same. The first word on the card contains control
information whose layout differs in the two formats.

Doug

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[COFF] Make your own virtual punchcard

[Charles H Sauer (he/him)]

https://boingboing.net/2025/03/10/make-your-own-virtual-punchcard.html

[50 years ago today I started working at IBM Yorktown. My boxes of 
punchcards from graduate work at UT-Austin were enroute with the movers 
from Austin, to be fed into VM-370 after they arrived. I wish I had kept 
those boxes as souvenirs.]

Charlie
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