![\"Braille](\"\/\/www.johndcook.com\/U288A.png\")
<\/p>\nBraille characters live in a 4×2 matrix. This means there are eight positions where the surface is either flat or raised. You can naturally denote a Braille character by an 8-bit binary number: the bit for a single position is either 0 for flat and 1 for raised.<\/p>\n
This is how Braille characters are encoded in Unicode. Braille characters are U+2800 through U+28FF, 2800 plus the binary number corresponding to the pattern of dots. However, there’s one surprise: the dots are numbered irregularly as indicated below:<\/p>\n
1 4
\n2 5
\n3 6
\n7 8<\/p>\n
Historically Braille had six cells, a 3×2 matrix, and the numbering made more sense: consecutive numbers, by column, left to right, the way Fortran stores matrices:<\/p>\n
1 4
\n2 5
\n3 6<\/p>\n
But when Braille was extended to a 4×2 matrix, the new positions were labeled 7 and 8 so as not to rename the previous positions.<\/p>\n
The numbered positions above correspond to the last eight bits of the Unicode character, from right to left. That is, position 1 determines the least significant bit and position 8 determines the 8th bit from the end.<\/p>\n
For example, here is Unicode character U+288A:<\/p>\n
<\/p>\n
The dots that are filled in correspond to positions 2, 4, and 8, so the last eight bits of the Unicode value are 10001010. The hexadecimal form of 10001010 is 8A, and the Unicode character is U+288A.<\/p>\n","protected":false},"excerpt":{"rendered":"
Braille characters live in a 4×2 matrix. This means there are eight positions where the surface is either flat or raised. You can naturally denote a Braille character by an 8-bit binary number: the bit for a single position is either 0 for flat and 1 for raised. This is how Braille characters are encoded […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[1],"tags":[],"class_list":["post-14248","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"acf":[],"aioseo_notices":[],"aioseo_head":"\n\t\t\n\t\n\t\n\t\n\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\n","aioseo_head_json":{"title":"Braille, Unicode, and binary","description":"Braille characters live in a 4x2 matrix. This means there are eight positions where the surface is either flat or raised. You can naturally denote a Braille character by an 8-bit binary number: the bit for a single position is either 0 for flat and 1 for raised. This is how Braille characters are encoded","canonical_url":"https:\/\/www.johndcook.com\/blog\/2014\/01\/15\/braille-unicode-and-binary\/","robots":"max-image-preview:large","keywords":"","webmasterTools":{"miscellaneous":""},"schema":null,"og:locale":"en_US","og:site_name":"John D. Cook | Applied Mathematics Consulting","og:type":"article","og:title":"Braille, Unicode, and binary","og:description":"Braille characters live in a 4x2 matrix. This means there are eight positions where the surface is either flat or raised. You can naturally denote a Braille character by an 8-bit binary number: the bit for a single position is either 0 for flat and 1 for raised. This is how Braille characters are encoded","og:url":"https:\/\/www.johndcook.com\/blog\/2014\/01\/15\/braille-unicode-and-binary\/","article:published_time":"2014-01-15T13:00:24+00:00","article:modified_time":"2017-01-21T01:33:18+00:00","twitter:card":"summary","twitter:title":"Braille, Unicode, and binary","twitter:description":"Braille characters live in a 4x2 matrix. This means there are eight positions where the surface is either flat or raised. You can naturally denote a Braille character by an 8-bit binary number: the bit for a single position is either 0 for flat and 1 for raised. This is how Braille characters are encoded","twitter:image":"https:\/\/www.johndcook.com\/blog\/wp-content\/uploads\/2022\/05\/twittercard.png"},"aioseo_meta_data":{"post_id":"14248","title":"Braille, Unicode, and binary","description":null,"keywords":null,"keyphrases":null,"primary_term":null,"canonical_url":null,"og_title":null,"og_description":null,"og_object_type":"default","og_image_type":"default","og_image_url":null,"og_image_width":null,"og_image_height":null,"og_image_custom_url":null,"og_image_custom_fields":null,"og_video":null,"og_custom_url":null,"og_article_section":null,"og_article_tags":null,"twitter_use_og":false,"twitter_card":"default","twitter_image_type":"default","twitter_image_url":null,"twitter_image_custom_url":null,"twitter_image_custom_fields":null,"twitter_title":null,"twitter_description":null,"schema":{"blockGraphs":[],"customGraphs":[],"default":{"data":{"Article":[],"Course":[],"Dataset":[],"FAQPage":[],"Movie":[],"Person":[],"Product":[],"ProductReview":[],"Car":[],"Recipe":[],"Service":[],"SoftwareApplication":[],"WebPage":[]},"graphName":"","isEnabled":true},"graphs":[]},"schema_type":null,"schema_type_options":null,"pillar_content":false,"robots_default":true,"robots_noindex":false,"robots_noarchive":false,"robots_nosnippet":false,"robots_nofollow":false,"robots_noimageindex":false,"robots_noodp":false,"robots_notranslate":false,"robots_max_snippet":null,"robots_max_videopreview":null,"robots_max_imagepreview":"large","priority":null,"frequency":null,"location":null,"local_seo":null,"breadcrumb_settings":null,"limit_modified_date":false,"created":"2020-12-21 02:38:39","updated":"2025-06-03 23:18:09","ai":null,"seo_analyzer_scan_date":null,"focus_keyword":null,"additional_keywords":null,"truseo_locale":null},"aioseo_breadcrumb":"