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For example, the binary number 100101 is converted to decimal form as follows: 100101 2 = [ ( 1 ) × 2 5 ] + [ ( 0 ) × 2 4 ] + [ ( 0 ) × 2 3 ] + [ ( 1 ) × 2 2 ] + [ ( 0 ) × 2 1 ] + [ ( 1 ) × 2 0 ]
In computer science, the double dabble algorithm is used to convert binary numbers into binary-coded decimal (BCD) notation. It is also known as the shift-and-add-3 algorithm, and can be implemented using a small number of gates in computer hardware, but at the expense of high latency.
In the decimal encoding, it is encoded as a series of p decimal digits (using the densely packed decimal (DPD) encoding). This makes conversion to decimal form efficient, but requires a specialized decimal ALU to process. In the binary integer decimal ( BID) encoding, it is encoded as a binary number.
In computing and electronic systems, binary-coded decimal (BCD) is a class of binary encodings of decimal numbers where each digit is represented by a fixed number of bits, usually four or eight. Sometimes, special bit patterns are used for a sign or other indications (e.g. error or overflow).
This table illustrates an example of decimal value of 149 and the location of LSb. In this particular example, the position of unit value (decimal 1 or 0) is located in bit position 0 (n = 0). MSb stands for most significant bit, while LSb stands for least significant bit. Binary (Decimal: 149) 1. 0.
Binary-coded decimal. Binary-coded decimal (BCD) is a binary encoded representation of integer values that uses a 4-bit nibble to encode decimal digits. Four binary bits can encode up to 16 distinct values; but, in BCD-encoded numbers, only ten values in each nibble are legal, and encode the decimal digits zero, through nine.
Computer engineers often need to write out binary quantities, but in practice writing out a binary number such as 1001001101010001 is tedious and prone to errors. Therefore, binary quantities are written in a base-8, or "octal", or, much more commonly, a base-16, "hexadecimal" (hex), number format. In the decimal system, there are 10 digits, 0 ...
Binary-to-decimal conversion with minimal number of digits. Converting a double-precision binary floating-point number to a decimal string is a common operation, but an algorithm producing results that are both accurate and minimal did not appear in print until 1990, with Steele and White's Dragon4. Some of the improvements since then include:
Decimal Binary Gray 0: 0000: 0000: 1: 0001: 0001: 2: 0010: 0011: 3: 0011: 0010: 4: 0100: 0110: 5: 0101: 0111: 6: 0110: 0101: 7: 0111: 0100: 8: 1000: 1100: 9: 1001: 1101: 10: 1010: 1111: 11: 1011: 1110: 12: 1100: 1010: 13: 1101: 1011: 14: 1110: 1001: 15: 1111: 1000
For writing numbers, the decimal system uses ten decimal digits, a decimal mark, and, for negative numbers, a minus sign "−". The decimal digits are 0 , 1 , 2, 3, 4, 5, 6, 7, 8, 9; [5] the decimal separator is the dot " . " in many countries (mostly English-speaking), [6] and a comma " , " in other countries.