NUMBRL

NUMBRL was originally intended for sighted people; however, it might also be a way for vision-impaired adults with an interest in numbers to begin to learn about braille or for both blind and sighted students to learn about number systems.

It is useful for beginners who want to become more familiar with the dot patterns or for anyone who wants a convenient analog way of representing the cells without using dot patterns directly.

NUMBRL is a numeric code that represents the dot patterns in braille cells; it is an alternative to listing the filled dot positions that some people find more useful.This page starts with an explanation of how to determine the NUMBRL codes for the braille cells. Tip! The explanation is followed by a number of very useful things you can do with this idea.

NUMBRL Codes


1-2-3-4-5-6
Cell positions.    		 10-20-40-1-2-4
Position values.
NUMBRL place values.

A NUMBRL code is easy to determine: you just look at a braille cell and sum up the NUMBRL values associated with its filled dot positions according to the diagram. (Note, do not sum the positions, sum the position values. )

Consider, for example, the cell with filled dot positions 1-3-5. The NUMBRL code for this cell is 10+40+2 = 52.

Dotless Braille Tip! NUMBRL is based on the binary and octal number systems. You don't need to know anything about these in order to use it, but if you are curious, you might want to check out this page.)

NUMBRL Practice

The practice chart to the right shows all 63 braille cells arranged in numerical order by their NUMBRL codes, which are printed under each cell.
Practice chart:
Braille cells with NUMBRL codes

For example, the square that is at the intersection of the row labeled 50 and the column labeled 02 has the inkprint dots for the Braille cell that has NUMBRL code 52. You can use this practice chart two ways:

(1) Practice calculating NUMBRL codes from dot patterns. If you have some braille text, pick any cell; otherwise just make one up. Calculate its NUMBRL code and use the code to locate the cell on the chart to see if you got it right. Note that when there aren't any dots in the left-hand column, a leading zero is used in the code so that all the codes will be two digits.

(2) Practice figuring out dot patterns from NUMBRL codes. Make up a NUMBRL code: it can be any two digit numeral using any of the digits from 0-7. Figure out what the dot pattern is before you look at the Chart! This is easier to do by columns. For example, if the code you made up is 25 then you know the left-hand column must only have a dot in the middle position because that one dot has the value 20. But there must be dots in both the top and bottom positions of the right-hand column since their values of one and four are the only way to add up to 5.

Making use of NUMBRL

The special value of NUMBRL is that it is not just a braille analog--which allows you to reconstruct the dot patterns--but a braille analog designed especially for humans: the two digits of the code for a cell are in the same left-to-right order as the cells' columns when the cells are read and the code is symmetric for the two columns.
Literary braille chart: Braille cells with meanings in order by NUMBRL codes.

Tip! The literary braille Find-A-Cell chart:


A code, 50, say, stands for the same dot pattern in the left-hand column of a cell as does a code 05 for the right-hand column.

The English Braille chart to the left shows all 63 braille cells again arranged in numerical order by their NUMBRL codes but with the English Braille meanings for the braille cells written under the cells. If you are a beginner, you've probably discovered that trying to find a particular braille cell by searching through all the cells the way they are usually arranged is difficult. Tip! However, if you know how to calculate a cell's NUMBRL code, you can easily find it in this chart.


Dotless Braille Tip! You can make your own customized NUMBRL charts with a word processor table. Once you are familiar with the code, it isn't even necessary to put the dot patterns in the squares in the table.This leaves more room for writing in notes about the different meanings that the various braille cells have in different contexts.

Dotless Braille Tip! Some sighted people use the NUMBRL codes to take Braille notes by hand because they find it easier to write these code numbers than either the regular dot position numbers or the actual dots.

Dotless Braille Tip! NUMBRL is also useful for making up your own Braille-English and English-Braille dictionaries which you can keep as Tables in a word processor.

(Most word processors let you sort tables so you can use the same table for both dictionaries; just change which column you are sorting on.) For words, you can just string together the codes for the letters. The cells in the logo are
"04-13-52-63-05-61 04-04-30-72-70". (Note that it is a good idea to put the leading zero in when there aren't any dots in the left-hand column of a cell since then all of the codes will have two digits and it is easier to check whether there are any mistakes.)

Dotless Braille Tip! NUMBRL is useful for six-key typing even if you don't know braille.

If you have a six-key brailler, stick labels above the keys for the NUMBRL position values as shown in the photo:

Old brailler with labeled keys.
label the keys from left to right with the numerals forty, twenty, ten, one, two, and four. Experiments have shown that sighted-grade school children can learn to correctly operate a brailler in under a minute--using a NUMBRL transcription--if you explain the need to simultaneously press all the keys required to sum up to each NUMBRL code. This might be an enjoyable and educational experience for sighted siblings and classmates of blind children--in fact, some might find a use for NUMBRL as the basis for a secret code or cipher.

Dotless Braille Tip! The arrangement of the cells in order by their NUMBRL codes shows the relationships among the dot patterns of the various cells in a different way. As you can see by the charts on this page, it is easier to find mirror-image pairs and other relationships in this arrangement than in the standard arrangment. Some people also find that this arrangement is helpful for memorizing the dot patterns.