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In digital electronics, a binary decoder is a combinational logic circuit that converts binary information from the n coded inputs to a maximum of 2 n unique outputs. They are used in a wide variety of applications, including instruction decoding, data multiplexing and data demultiplexing, seven segment displays, and as address decoders for memory and port-mapped I/O.
For example, a packed decimal value encoded with the bytes 12 34 56 7C represents the fixed-point value +1,234.567 when the implied decimal point is located between the fourth and fifth digits: 12 34 56 7C 12 34.56 7+ The decimal point is not actually stored in memory, as the packed BCD storage format does not provide for it.
Densely packed decimal (DPD) is an efficient method for binary encoding decimal digits.. The traditional system of binary encoding for decimal digits, known as binary-coded decimal (BCD), uses four bits to encode each digit, resulting in significant wastage of binary data bandwidth (since four bits can store 16 states and are being used to store only 10), even when using packed BCD.
For example, the hexadecimal representation of the 24 bits above is 4D616E. The octal representation is 23260556. Those 8 octal digits can be split into pairs (23 26 05 56), and each pair is converted to decimal to yield 19 22 05 46. Using those four decimal numbers as indices for the Base64 alphabet, the corresponding ASCII characters are TWFu.
Chen–Ho encoding is a memory-efficient alternate system of binary encoding for decimal digits.. The traditional system of binary encoding for decimal digits, known as binary-coded decimal (BCD), uses four bits to encode each digit, resulting in significant wastage of binary data bandwidth (since four bits can store 16 states and are being used to store only 10), [1] even when using packed BCD.
In IEEE 754 parlance, there are 10 bits of significand, but there are 11 bits of significand precision (log 10 (2 11) ≈ 3.311 decimal digits, or 4 digits ± slightly less than 5 units in the last place).
A binary clock might use LEDs to express binary values. In this clock, each column of LEDs shows a binary-coded decimal numeral of the traditional sexagesimal time.. The common names are derived somewhat arbitrarily from a mix of Latin and Greek, in some cases including roots from both languages within a single name. [27]
The primary advantage of excess-3 coding over non-biased coding is that a decimal number can be nines' complemented [1] (for subtraction) as easily as a binary number can be ones' complemented: just by inverting all bits. [1] Also, when the sum of two excess-3 digits is greater than 9, the carry bit of a 4-bit adder will be set high.