Log in or Sign up
Coin Talk
Home
Forums
>
Coin Forums
>
Paper Money
>
Plate position arithmetic
>
Reply to Thread
Message:
<p>[QUOTE="Numbers, post: 560865, member: 11668"]Okay, you folks asked for it.... Here's how to calculate plate positions on modern U.S. notes. It's going to be math-heavy; don't say I didn't warn you.... <img src="styles/default/xenforo/clear.png" class="mceSmilieSprite mceSmilie6" alt=":cool:" unselectable="on" unselectable="on" /></p><p><br /></p><p>First of all, to avoid some complications, let's assume the note is (a) dated 1990 or later, (b) denominated $1 through $20, and (c) not a star note, uncut sheet note, or similar. (I'll cover these other cases later.)</p><p><br /></p><p>Currency is printed in sheets of 32 notes, and in print runs of 200,000 sheets (=6,400,000 notes). The notes on each sheet are *not* consecutive; rather, consecutive notes come from the same position on different sheets. That way, the BEP can take a stack of 100 sheets, run the whole stack through a guillotine cutter, and cut it directly into a bunch of ready-to-package 100-note straps--there's no need to sort and stack the notes after they've been cut.</p><p><br /></p><p>The serial numbering in each plate position runs consecutively through the entire 200,000-sheet print run. So in the first run of a block (for example), serial numbers 00000001 through 00200000 will be printed in position A1 of the 200,000 sheets. Serials 00200001 through 00400000 will be printed in position B1, and so on, until serials 06200001 through 06400000 are printed in position H4. Then the cycle starts over again in the next print run. A total of 15 of these print runs brings the numbering up to 96000000, at which point there aren't enough serials left for another whole run, so the numbering then moves on to the next block. (This is why serials above 96000000 aren't used these days.)</p><p><br /></p><p>The upshot of this is that, if you look at all the notes in serial order, the plate position only changes once every 200,000 serials, and it cycles through the 32 possible positions once every 6,400,000 serials. So to calculate the correct plate position for a given serial number, you do the following:</p><p><br /></p><p>1. Divide the serial number by 6,400,000. Discard the quotient and keep only the remainder.</p><p>2. Divide that remainder by 200,000, and round the answer *up* to a whole number. (Note that you *always* round up, even if the decimal is less than 1/2.)</p><p>3. You now have a number from 1 to 32, which corresponds to the plate position. Numbers 1 to 8 are positions A1 to H1; numbers 9 to 16 are positions A2 to H2; numbers 17 to 24 are positions A3 to H3; and numbers 25 to 32 are positions A4 to H4.</p><p><br /></p><p>For example, if the serial number is 87654321, then dividing by 6,400,000 gives 13 with a remainder of 4454321. Dividing 4454321 by 200,000 gives about 22.27, which rounds up to 23. Thus this serial number belongs in position G3.</p><p><br /></p><p>If you've got a calculator that doesn't have a divide-with-remainder function, then the steps can be restated this way: Divide the serial by 6,400,000; subtract the whole-number part of the answer, leaving only the decimal; multiply by 32; and round up to a whole number. So for example 87654321 divided by 6,400,000 is 13.695988; subtracting off the 13 leaves 0.695988; and multiplying by 32 gives about 22.27, which rounds up to 23, as above.</p><p><br /></p><p>There's one potential complication still: the BEP actually cuts the 32-note sheets in half vertically, into 16-note pieces, before running them through the numbering presses. It's possible, though somewhat uncommon, for a half-sheet to end up in the "wrong" pile--a left half on the right side of the press, or a right half on the left side. When this happens, the plate position will be off by 16 places, meaning that the number 1 might be swapped for 3, or 2 might be swapped for 4. (So our example serial number 87654321 *should* have position G3, as calculated above, but *might* have position G1 instead.) Swaps like this aren't considered errors, since the BEP doesn't really mind them, but as a percentage of all notes they're pretty uncommon.</p><p><br /></p><p><b>$50's, $100's, and older notes</b></p><p><br /></p><p>Okay, the above discussion is great for anything printed in 6,400,000-note standard runs. What about other run sizes? Current-series $50's and $100's, as well as lower-denomination notes printed from about 1984 to 1989, used runs of 3,200,000 notes (=100,000 sheets) instead. The effect on the calculations is that you need to replace 6,400,000 by 3,200,000, and replace 200,000 by 100,000. Everything else still works just the same.</p><p><br /></p><p>So if that serial number 87654321 were found on a $50 note, or on a 1985 $1, then the calculation would look like this: 87654321 divided by 3,200,000 is 27.391975; subtracting off the 27 leaves 0.391975; and multiplying by 32 gives 12.54, which rounds up to 13. So this note should have plate position E2 (but might be E4 instead).</p><p><br /></p><p>(Incidentally, when there are only 3,200,000 notes per print run, the BEP can fit 31 print runs per block, leading to a maximum serial number of 99200000. That's why $50's and $100's use higher serials than the other denominations do, and why serials higher than 96000000 can be found on older notes of all denominations.)</p><p><br /></p><p>Even earlier, print runs of various other, shorter lengths were used. And before Series 1957, the sheet size was different too: there were 18 notes per sheet (with the 18 positions labelled with single letters A through R). Possible run sizes over the years have included 1,280,000 notes (=40,000 sheets of 32); 640,000 notes (=20,000 sheets of 32); 256,000 notes (=8000 sheets of 32); 360,000 notes (=20,000 sheets of 18); and 144,000 notes (=8000 sheets of 18). The changes from one run size to another happened at different times for different denominations and types of currency, often in the middle of a series. So if you want to calculate a plate position on an older note, you'll first need to determine the correct print run standard from the mostly-complete table <a href="http://www.uspapermoney.info/general/runs.html" target="_blank" class="externalLink ProxyLink" data-proxy-href="http://www.uspapermoney.info/general/runs.html" rel="nofollow">here</a>.</p><p><br /></p><p>Once you've done that, the calculation proceeds much as above: <span style="color: DarkGreen">Divide the serial number by the number of notes in a standard print run; subtract off the whole-number part of the answer, leaving only the decimal; multiply by the number of notes printed per sheet; round *up* to a whole number; and convert that number to a plate position.</span></p><p><br /></p><p>So for one more example, let's suppose that we've got a 1953 $5 silver certificate with serial number A87654321A. It's dated before 1957, so it was printed on an 18-note sheet, and the table shows that the appropriate standard print run is 20,000 sheets, or 360,000 notes. So we divide 87654321 by 360,000, obtaining 243.48423; subtract off the 243, leaving 0.48423; multiply by 18, obtaining about 8.72; and round up to 9. Thus this note comes from the 9th position on the sheet, position I. (And the 18-note sheets weren't cut before numbering, so I is the only possibility.)</p><p><br /></p><p>If you go back a few more years, before about 1952, everything was printed in sheets of 12 notes, which were numbered in a completely different way. So none of the above will apply to notes printed in sheets of 12.</p><p><br /></p><p><b>Star notes, uncut sheet notes, &c.</b></p><p><br /></p><p>Incredibly, these are even more complicated. I'll come back to them when I've got time to make another gimungous post.... <img src="styles/default/xenforo/clear.png" class="mceSmilieSprite mceSmilie11" alt=":rolleyes:" unselectable="on" unselectable="on" /></p><p><br /></p><p>Meanwhile, if you're getting sick of doing all this arithmetic, <a href="http://snorkack.nfshost.com/orph/serial-calc.xls" target="_blank" class="externalLink ProxyLink" data-proxy-href="http://snorkack.nfshost.com/orph/serial-calc.xls" rel="nofollow">here</a>'s an Excel sheet I rigged up that'll do the work for you.[/QUOTE]</p><p><br /></p>
[QUOTE="Numbers, post: 560865, member: 11668"]Okay, you folks asked for it.... Here's how to calculate plate positions on modern U.S. notes. It's going to be math-heavy; don't say I didn't warn you.... :cool: First of all, to avoid some complications, let's assume the note is (a) dated 1990 or later, (b) denominated $1 through $20, and (c) not a star note, uncut sheet note, or similar. (I'll cover these other cases later.) Currency is printed in sheets of 32 notes, and in print runs of 200,000 sheets (=6,400,000 notes). The notes on each sheet are *not* consecutive; rather, consecutive notes come from the same position on different sheets. That way, the BEP can take a stack of 100 sheets, run the whole stack through a guillotine cutter, and cut it directly into a bunch of ready-to-package 100-note straps--there's no need to sort and stack the notes after they've been cut. The serial numbering in each plate position runs consecutively through the entire 200,000-sheet print run. So in the first run of a block (for example), serial numbers 00000001 through 00200000 will be printed in position A1 of the 200,000 sheets. Serials 00200001 through 00400000 will be printed in position B1, and so on, until serials 06200001 through 06400000 are printed in position H4. Then the cycle starts over again in the next print run. A total of 15 of these print runs brings the numbering up to 96000000, at which point there aren't enough serials left for another whole run, so the numbering then moves on to the next block. (This is why serials above 96000000 aren't used these days.) The upshot of this is that, if you look at all the notes in serial order, the plate position only changes once every 200,000 serials, and it cycles through the 32 possible positions once every 6,400,000 serials. So to calculate the correct plate position for a given serial number, you do the following: 1. Divide the serial number by 6,400,000. Discard the quotient and keep only the remainder. 2. Divide that remainder by 200,000, and round the answer *up* to a whole number. (Note that you *always* round up, even if the decimal is less than 1/2.) 3. You now have a number from 1 to 32, which corresponds to the plate position. Numbers 1 to 8 are positions A1 to H1; numbers 9 to 16 are positions A2 to H2; numbers 17 to 24 are positions A3 to H3; and numbers 25 to 32 are positions A4 to H4. For example, if the serial number is 87654321, then dividing by 6,400,000 gives 13 with a remainder of 4454321. Dividing 4454321 by 200,000 gives about 22.27, which rounds up to 23. Thus this serial number belongs in position G3. If you've got a calculator that doesn't have a divide-with-remainder function, then the steps can be restated this way: Divide the serial by 6,400,000; subtract the whole-number part of the answer, leaving only the decimal; multiply by 32; and round up to a whole number. So for example 87654321 divided by 6,400,000 is 13.695988; subtracting off the 13 leaves 0.695988; and multiplying by 32 gives about 22.27, which rounds up to 23, as above. There's one potential complication still: the BEP actually cuts the 32-note sheets in half vertically, into 16-note pieces, before running them through the numbering presses. It's possible, though somewhat uncommon, for a half-sheet to end up in the "wrong" pile--a left half on the right side of the press, or a right half on the left side. When this happens, the plate position will be off by 16 places, meaning that the number 1 might be swapped for 3, or 2 might be swapped for 4. (So our example serial number 87654321 *should* have position G3, as calculated above, but *might* have position G1 instead.) Swaps like this aren't considered errors, since the BEP doesn't really mind them, but as a percentage of all notes they're pretty uncommon. [B]$50's, $100's, and older notes[/B] Okay, the above discussion is great for anything printed in 6,400,000-note standard runs. What about other run sizes? Current-series $50's and $100's, as well as lower-denomination notes printed from about 1984 to 1989, used runs of 3,200,000 notes (=100,000 sheets) instead. The effect on the calculations is that you need to replace 6,400,000 by 3,200,000, and replace 200,000 by 100,000. Everything else still works just the same. So if that serial number 87654321 were found on a $50 note, or on a 1985 $1, then the calculation would look like this: 87654321 divided by 3,200,000 is 27.391975; subtracting off the 27 leaves 0.391975; and multiplying by 32 gives 12.54, which rounds up to 13. So this note should have plate position E2 (but might be E4 instead). (Incidentally, when there are only 3,200,000 notes per print run, the BEP can fit 31 print runs per block, leading to a maximum serial number of 99200000. That's why $50's and $100's use higher serials than the other denominations do, and why serials higher than 96000000 can be found on older notes of all denominations.) Even earlier, print runs of various other, shorter lengths were used. And before Series 1957, the sheet size was different too: there were 18 notes per sheet (with the 18 positions labelled with single letters A through R). Possible run sizes over the years have included 1,280,000 notes (=40,000 sheets of 32); 640,000 notes (=20,000 sheets of 32); 256,000 notes (=8000 sheets of 32); 360,000 notes (=20,000 sheets of 18); and 144,000 notes (=8000 sheets of 18). The changes from one run size to another happened at different times for different denominations and types of currency, often in the middle of a series. So if you want to calculate a plate position on an older note, you'll first need to determine the correct print run standard from the mostly-complete table [URL="http://www.uspapermoney.info/general/runs.html"]here[/URL]. Once you've done that, the calculation proceeds much as above: [COLOR=DarkGreen]Divide the serial number by the number of notes in a standard print run; subtract off the whole-number part of the answer, leaving only the decimal; multiply by the number of notes printed per sheet; round *up* to a whole number; and convert that number to a plate position.[/COLOR] So for one more example, let's suppose that we've got a 1953 $5 silver certificate with serial number A87654321A. It's dated before 1957, so it was printed on an 18-note sheet, and the table shows that the appropriate standard print run is 20,000 sheets, or 360,000 notes. So we divide 87654321 by 360,000, obtaining 243.48423; subtract off the 243, leaving 0.48423; multiply by 18, obtaining about 8.72; and round up to 9. Thus this note comes from the 9th position on the sheet, position I. (And the 18-note sheets weren't cut before numbering, so I is the only possibility.) If you go back a few more years, before about 1952, everything was printed in sheets of 12 notes, which were numbered in a completely different way. So none of the above will apply to notes printed in sheets of 12. [B]Star notes, uncut sheet notes, &c.[/B] Incredibly, these are even more complicated. I'll come back to them when I've got time to make another gimungous post.... :rolleyes: Meanwhile, if you're getting sick of doing all this arithmetic, [URL="http://snorkack.nfshost.com/orph/serial-calc.xls"]here[/URL]'s an Excel sheet I rigged up that'll do the work for you.[/QUOTE]
Your name or email address:
Do you already have an account?
No, create an account now.
Yes, my password is:
Forgot your password?
Stay logged in
Coin Talk
Home
Forums
>
Coin Forums
>
Paper Money
>
Plate position arithmetic
>
Home
Home
Quick Links
Search Forums
Recent Activity
Recent Posts
Forums
Forums
Quick Links
Search Forums
Recent Posts
Competitions
Competitions
Quick Links
Competition Index
Rules, Terms & Conditions
Gallery
Gallery
Quick Links
Search Media
New Media
Showcase
Showcase
Quick Links
Search Items
Most Active Members
New Items
Directory
Directory
Quick Links
Directory Home
New Listings
Members
Members
Quick Links
Notable Members
Current Visitors
Recent Activity
New Profile Posts
Sponsors
Menu
Search
Search titles only
Posted by Member:
Separate names with a comma.
Newer Than:
Search this thread only
Search this forum only
Display results as threads
Useful Searches
Recent Posts
More...
