Codice binario 4 bit
In computing and electronic systems, binary-coded decimal BCD is a class of binary encodings of decimal numbers where each decimal digit is represented by a fixed number of bitsusually four or eight.
Special bit patterns are sometimes used for a sign or for other indications e. In byte-oriented systems i. The precise 4-bit encoding may vary however, for technical reasons, see Excess-3 for instance. BCD's main virtue is its more accurate representation and rounding of decimal quantities as well as an ease of conversion into human-readable representations, in comparison to binary positional systems. BCD's principal drawbacks are a small increase in the complexity of the circuits needed to implement basic arithmetics and a slightly less dense storage.
Although BCD per se is not as widely used as in the past and is no longer implemented in newer computers' instruction sets such as ARM ; x86 does not support BCD instructions in long mode any moredecimal fixed-point and floating-point formats are still important and continue to be used in financial, commercial, and industrial computing, where subtle conversion and fractional rounding errors that are inherent in floating point binary representations cannot be tolerated.
BCD codice binario 4 bit advantage of the codice binario 4 bit that any one decimal numeral can be represented by codice binario 4 bit four bit pattern. The most obvious way of encoding digits is "natural BCD" NBCDwhere each decimal digit is represented by its corresponding four-bit binary value, as shown in the following table. This is also called "" encoding. Other encodings are also used, including so-called "" and ""—named after the weighting used for the bits—and " Excess-3 ".
As most computers deal with data in 8-bit codice binario 4 bitit is possible to use one of the following methods to encode a Codice binario 4 bit number:. As an example, encoding the decimal number 91 using unpacked BCD results in the following binary pattern of two bytes:. Hence the numerical range for one unpacked BCD byte is zero through nine inclusive, whereas the range for one packed BCD is zero through ninety-nine inclusive. To represent numbers larger than the range of a single byte any number of contiguous bytes may be used.
For example, to represent the decimal number in packed BCD, using big-endian format, a program would encode as follows:. Note that the most significant nibble of the most significant codice binario 4 bit is zero, implying that the number is in actuality Also note how packed BCD is more efficient in storage usage as compared to unpacked BCD; encoding the same number with the leading zero in unpacked format would consume twice the storage.
Shifting and masking operations are used to pack or unpack a packed BCD digit. Other logical operations are used to codice binario 4 bit a numeral to its equivalent bit pattern or reverse the process. BCD is very common in electronic systems where a numeric value is to be displayed, especially in systems consisting solely of digital logic, and not containing a microprocessor.
By employing BCD, the manipulation of numerical data for display can be greatly simplified by treating each digit as a separate single sub-circuit.
This matches much more closely the physical reality of display hardware—a designer might choose to use a series of separate identical seven-segment displays to build a metering circuit, for example. If the numeric quantity were stored and manipulated as pure binary, interfacing to such a display would require complex circuitry.
Therefore, in cases where the calculations are relatively simple, working throughout with BCD can lead to a simpler overall system than converting to and from binary. Most pocket calculators do all their calculations in BCD.
The same argument applies when hardware of this type uses an embedded microcontroller or other small processor. Often, smaller code results when representing numbers internally in BCD format, since a conversion from or to binary representation can be expensive on such limited processors. Codice binario 4 bit these applications, some small processors feature BCD arithmetic modes, which assist when writing routines that manipulate BCD quantities.
In packed BCD or simply packed decimaleach of the two nibbles of each byte represent a decimal digit. Most implementations are big endiani. The lower nibble of the rightmost byte is usually used as the sign flag, although some unsigned representations lack a sign flag. As an example, a 4-byte value consists of 8 nibbles, wherein the upper 7 nibbles store the digits of a 7-digit decimal value and the lowest nibble indicates the sign of the decimal integer value.
Other allowed signs are A and E for positive and B for negative. Most implementations also provide unsigned BCD values with a sign nibble of F. Burroughs systems used D for negative, and any other value is considered a positive sign value the processors will normalize a positive sign to C. No matter how many bytes wide a word is, there are always an even number of nibbles because each byte has two of them.
Note that, like character strings, the first byte of the packed decimal — with the most significant two digits — is usually stored in the lowest address in memory, independent of the endianness of the machine. The extra storage requirements are usually offset by the need for the accuracy and compatibility with calculator or hand calculation that fixed-point decimal arithmetic provides.
Denser packings of BCD exist which avoid the storage penalty and also codice binario 4 bit no arithmetic operations for common conversions. Ten's complement representations for negative numbers offer an alternative approach to encoding the sign of packed and other BCD numbers. In this case, positive numbers always have a most significant digit between 0 and 4 inclusivewhile negative numbers are represented by the 10's complement of the corresponding positive number.
As a result, this system allows for, a bit packed BCD numbers to range from , to 49,, and -1 is represented codice binario 4 bit As with two's complement binary numbers, the range is codice binario 4 bit symmetric about zero. These languages allow the programmer to specify an implicit decimal point in front of one of the digits.
The decimal point is not actually stored in memory, as the packed BCD storage format does not provide for it. Its location is simply known to the compiler and the generated code acts accordingly for the various arithmetic operations. If a decimal digit requires four bits, then three decimal digits require 12 bits.
However, since 2 10 1, is greater than 10 3 1,if three decimal digits are encoded together, codice binario 4 bit 10 bits are needed. The latter has the advantage that subsets of the encoding encode two digits in the codice binario 4 bit seven bits and one digit in four bits, as in regular BCD. Some implementations, for example IBM mainframe systems, support zoned decimal numeric representations.
Each decimal digit is stored in one byte, with the lower four bits encoding the digit in BCD form. The upper four bits, called the "zone" bits, are usually set to a fixed value so that the byte holds a character value corresponding to the digit.
For signed zoned decimal values, the rightmost least significant zone nibble holds the sign digit, which is the same set of values that are used for signed packed decimal numbers see above. These characters vary depending on the local character code page setting.
The IBM series are codice binario 4 bit machines, each location being six bits labeled B, A, 8, 4, 2 and 1, plus an odd parity check bit C and a word mark bit M.
For codice binario 4 bit digits 1 through 9B and A are zero and the digit value represented by standard 4-bit BCD in bits 8 through 1. For most other characters bits B and A are derived simply from codice binario 4 bit "12", "11", and "0" "zone codice binario 4 bit in the punched card character code, and bits 8 through 1 from the 1 through 9 punches.
A "12 zone" punch set both B and Aan "11 zone" set Band a "0 zone" a 0 punch combined with any others set A. Thus the letter Awhich is 12,1 in the punched card format, is encoded B,A,1. This allows the circuitry to convert between the punched card format and the internal storage format to be very simple with only a few special cases.
One important special case is digit 0represented by a lone 0 punch in the card, and 8,2 in core memory. The memory of the IBM is organized into 6-bit addressable digits, the usual 8, 4, 2, 1 plus Fused as a flag bit and Can odd parity check bit. BCD alphamerics are encoded using digit pairs, with the "zone" in the even-addressed digit and the "digit" in the odd-addressed digit, the "zone" being related to the 1211and 0 "zone punches" as in the series. A variable length Packed BCD numeric data type is also implemented, providing machine instructions that perform arithmetic directly on codice binario 4 bit decimal data.
All of these are used within hardware registers and processing units, and in software. The MicroVAX and later VAX implementations dropped this ability from the CPU but retained code compatibility with earlier codice binario 4 bit by implementing the missing instructions in an operating system-supplied software library. This is invoked automatically via exception handling when the no longer implemented codice binario 4 bit are encountered, so that programs using them can execute without modification on the newer machines.
The Intel x86 architecture supports a unique digit ten-byte BCD format that can be loaded into and stored from the floating point registers, and computations can be performed there. The Motorola series had BCD instructions. In more recent computers such capabilities are almost always codice binario 4 bit in software rather than the CPU's instruction set, but BCD numeric data is still extremely common in commercial and financial applications.
There are tricks for implementing packed BCD and zoned decimal add or subtract operations using short but difficult to understand sequences of word-parallel logic and binary arithmetic operations.
Conversion of the simple sum of two digits can be done by adding 6 that is, 16 — 10 when the five-bit result of adding a pair of digits has a value greater than 9. Note that is the binary, not decimal, representation of the desired result. Also note that it cannot fit in a 4-bit number. In BCD as in decimal, there cannot exist a value greater than 9 per digit. To correct this, 6 is added to that sum and then the result is treated as two nibbles:.
The two nibbles of the result, andcorrespond to the digits "1" and "7". This yields "17" in BCD, which is the correct result. This technique can be extended to adding multiple digits by adding in groups from right to left, propagating the second digit as a carry, always comparing the 5-bit result of each digit-pair sum to 9.
Some CPUs provide a half-carry flag to facilitate BCD arithmetic adjustments following binary addition and subtraction operations. Subtraction is done by adding the ten's codice binario 4 bit of the subtrahend.
To represent the sign of a number in BCD, the number is used to represent a positive numberand is used to represent a negative number. The remaining 14 combinations are invalid signs. To illustrate signed Codice binario 4 bit subtraction, consider the following problem: In signed BCD, is The ten's complement of can be obtained by taking the nine's complement ofand then adding one. Since BCD is a form of decimal representation, several of the digit sums above are invalid.
In the event that an invalid entry any BCD digit greater than exists, 6 is added to generate a carry bit and cause the sum to become a valid entry. So adding 6 to the invalid entries results in the following:. To check the answer, note that the first digit is 9, which means negative. To check the rest of the digits, represent them in decimal.
The binary-coded decimal scheme described in this article is the most common encoding, but there are many others. The following table represents decimal digits from 0 to 9 in various BCD systems:. In the case Gottschalk v. Bensonthe U. Supreme Court overturned a lower court decision which had allowed a patent for converting BCD encoded numbers to binary on a computer. This was an important case in determining the patentability of software and algorithms. The Atari 8-bit family of computers used BCD to implement floating-point algorithms.
A binary code represents textcomputer processor instructionsor other data codice binario 4 bit any two-symbol system, but often the binary number system 's 0 and 1. The binary code assigns a pattern of binary digits bits to each character, instruction, etc. For example, a binary string of eight bits can represent any of possible values and can therefore represent a variety of different items. In computing and telecommunications, binary codes are used for various methods of encoding codice binario 4 bit, such as character stringsinto bit strings.
Those methods may use fixed-width or variable-width strings. In a fixed-width binary code, each letter, digit, or other character is represented by a bit string of the same length; that bit string, interpreted as a binary numberis usually displayed in code tables in octaldecimal or hexadecimal notation.
There are many character sets and many character encodings for them. A bit string, interpreted as a binary number, can be translated into a decimal number. For example, the lower case aif represented by the bit string as it is in the standard ASCII codecan also be represented as the decimal number The full title is translated into English as the "Explanation of the binary arithmetic", which uses only the characters 1 and 0, with some remarks on its usefulness, and on the light it throws on the ancient Chinese figures of Fu Xi.
Leibniz's system uses codice binario 4 bit and 1, like the modern binary numeral system. Leibniz encountered the I Ching through French Jesuit Joachim Bouvet and noted with fascination how its hexagrams correspond to the binary numbers from 0 toand concluded that this mapping was evidence of major Chinese accomplishments codice binario 4 bit the sort of philosophical mathematics he admired.
Binary numerals were central to Leibniz's theology. He believed codice binario 4 bit binary numbers were symbolic of the Christian idea of creatio ex nihilo or creation out of nothing.
The book had confirmed his theory that life could be simplified or reduced down to a series of straightforward propositions. He created a system consisting of rows of zeros and ones.
During this time period, Leibniz had not yet found a use for codice binario 4 bit system. Binary systems predating Leibniz also existed in the ancient world. The residents of the island of Mangareva in French Polynesia were using a hybrid binary- decimal codice binario 4 bit before The ordering is also the lexicographical order on sextuples of elements chosen from a two-element set.
In Francis Bacon discussed a system whereby letters of the alphabet could be reduced to sequences of binary digits, which could then be encoded as scarcely visible variations in the font in any random text. Another mathematician and philosopher by the name of George Boole published a paper in called 'The Mathematical Codice binario 4 bit of Logic' that describes an algebraic system of logic, now known as Boolean algebra.
Shannon wrote his thesis inwhich implemented his findings. Shannon's thesis became a starting point for the use of the binary code in practical applications such as computers, electric circuits, and more. The bit string is not the only type of binary code.
A binary system in general is any system that allows only two choices such as a switch in an electronic system or a simple true or false test. Braille is a type of binary code that is widely used by blind people to read and write by touch, named for its creator, Louis Braille. This system consists of grids of six dots each, three per column, in which each dot has two states: The different combinations of raised and flattened dots are capable of representing all letters, numbers, and punctuation signs.
The bagua are diagrams used in feng shuiTaoist cosmology and I Ching studies. The relationships between the trigrams are represented in two arrangements, the primordial, "Earlier Heaven" or "Fuxi" baguaand the manifested, "Later Heaven,"or "King Wen" bagua. In Yoruba religionthe rite provides a means of communication with spiritual divinity. In wood powder, these are recorded as single and codice binario 4 bit lines. The American Standard Code for Information Interchange ASCIIuses a 7-bit binary code to represent text and other characters within computers, communications equipment, and other devices.
Each letter or symbol is assigned a number from 0 to For example, lowercase "a" is represented by codice binario 4 bit a bit string which is 97 in decimal.
Binary-coded decimalor 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 the first ten values in each nibble are legal, and encode the decimal digits zero, through nine.
The remaining six values are illegal, and may cause either a machine exception or unspecified behavior, depending on the computer implementation of BCD arithmetic. BCD arithmetic is sometimes preferred to floating-point numeric formats in commercial and financial applications where the complex rounding behaviors of floating-point numbers is inappropriate. Most modern computers use binary encoding for instructions and data.
Telephone calls are carried digitally on codice binario 4 bit and mobile phone networks using pulse-code modulationand on voice over IP networks. The weight of a binary code, as defined in the table of constant-weight codes is the Hamming weight of the binary words coding for the represented words or sequences. From Wikipedia, the free encyclopedia. This section has multiple issues. Please help improve it or discuss these issues on the talk page.
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Statements consisting only of original research should be removed. March Learn codice binario 4 bit and when to remove this template codice binario 4 bit. List of binary codes. Gerhardt, Berlinvol. What Kind of Rationalist?: What Kind of Rationalist? Leibniz, Mysticism and Religion.
Proceedings of the National Academy of Sciences. Codice binario 4 bit East and West. University of Hawaii Press. The I Ching or Book of Changes. Baynes, forward by C.
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