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If a decimal digit requires four bits, then three decimal digits require 12 bits. However, since 2 10 (1,024) is greater than 10 3 (1,000), if three decimal digits are encoded together, only 10 bits are needed. Two such encodings are Chen–Ho encoding and densely packed decimal (DPD). The latter has the advantage that subsets of the encoding ...
For instance, using a 32-bit format, 16 bits may be used for the integer and 16 for the fraction. The eight's bit is followed by the four's bit, then the two's bit, then the one's bit. The fractional bits continue the pattern set by the integer bits. The next bit is the half's bit, then the quarter's bit, then the ⅛'s bit, and so on. For example:
Using the fact that 2 10 = 1024 is only slightly more than 10 3 = 1000, 3n-digit decimal numbers can be efficiently packed into 10n binary bits. However, the IEEE formats have significands of 3n+1 digits, which would generally require 10n+4 binary bits to represent.
There are many character sets and many character encodings for them. Binary to Hexadecimal or Decimal. A bit string, interpreted as a binary number, can be translated into a decimal number. For example, the lower case a, if represented by the bit string 01100001 (as it is in the standard ASCII code), can also be represented as the decimal ...
The 8 decimal values whose digits are all 8s or 9s have four codings each. The bits marked x in the table above are ignored on input, but will always be 0 in computed results. (The 8 × 3 = 24 non-standard encodings fill the unused range from 10 3 = 1000 to 2 10 - 1 = 1023.)
Thus, only 10 bits of the significand appear in the memory format but the total precision is 11 bits. 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).
The byte is a unit of digital information that most commonly consists of eight bits. 1 byte (B) = 8 bits (bit).Historically, the byte was the number of bits used to encode a single character of text in a computer [1] [2] and for this reason it is the smallest addressable unit of memory in many computer architectures.
This table illustrates an example of an 8 bit signed decimal value using the two's complement method. The MSb most significant bit has a negative weight in signed integers, in this case -2 7 = -128. The other bits have positive weights. The lsb (least significant bit) has weight 2 0 =1. The signed value is in this case -128+2 = -126.
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