{"id":54,"date":"2019-09-10T06:38:21","date_gmt":"2019-09-10T06:38:21","guid":{"rendered":"http:\/\/learnlearn.uk\/alevelcs\/?page_id=54"},"modified":"2020-09-22T01:12:34","modified_gmt":"2020-09-22T01:12:34","slug":"binary-coded-decimal","status":"publish","type":"page","link":"https:\/\/learnlearn.uk\/alevelcs\/binary-coded-decimal\/","title":{"rendered":"Binary Coded Decimal"},"content":{"rendered":"
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Introduction<\/h2>\n
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What is Binary Coded Decimal<\/h2>\n

Binary Coded Decimal is a form of binary representation where each denary digit is converted individually into binary, rather than the whole number being converted as a large number.<\/p>\n

Example 1 – the number 42<\/h3>\n

Normally this number would be converted directed to binary as 00101010<\/strong>\u00a0 as 8 bit binary.<\/p>\n\n\n\n\n\n\n\n\n\n<\/colgroup>\n\n\n\n
128<\/strong><\/td>\n64<\/strong><\/td>\n32<\/strong><\/td>\n16<\/strong><\/td>\n8<\/strong><\/td>\n4<\/strong><\/td>\n2<\/strong><\/td>\n1<\/strong><\/td>\n<\/tr>\n
0<\/td>\n0<\/td>\n1<\/td>\n0<\/td>\n1<\/td>\n0<\/td>\n1<\/td>\n0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

However in binary coded decimal we would convert the number 4 to binary and the number 2 to binary, then simply concatenate(combine) the 2 numbers together<\/p>\n

Binary 4<\/strong><\/p>\n\n\n\n\n\n<\/colgroup>\n\n\n\n
8<\/strong><\/td>\n4<\/strong><\/td>\n2<\/strong><\/td>\n1<\/strong><\/td>\n<\/tr>\n
0<\/td>\n1<\/td>\n0<\/td>\n0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Binary 2<\/strong><\/p>\n\n\n\n\n\n<\/colgroup>\n\n\n\n
8<\/strong><\/td>\n4<\/strong><\/td>\n2<\/strong><\/td>\n1<\/strong><\/td>\n<\/tr>\n
0<\/td>\n0<\/td>\n1<\/td>\n0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

 <\/p>\n

Therefore 42 in BCD binary would be 01000010<\/strong><\/p>\n\n<\/div>

Why use BCD?<\/h2>\n
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Why use Binary Coded Decimal?<\/h3>\n

Binary coded decimal has 3 main advantages<\/p>\n

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  • It is easier for a human to read large binary numbers than if the number is in pure binary<\/li>\n
  • It is simpler to create hardware than only counts in decimal and uses basic calculation (e.g. digital clocks, simple handheld calculators)<\/li>\n
  • Binary coded decimal removes the problem of floating point rounding errors, which makes is very useful for handling financial transactions.<\/li>\n<\/ul>\n

     <\/p>\n

     <\/p>\n\n<\/div>

    BCD Clock Demo<\/h2>\n
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    Binary Coded Decimal Clock Demonstration Project<\/h3>\n

    The Scratch project for this clock can be found here<\/a><\/p>\n