Binary coded decimal number, referred to as BCD code (Binarycoded Decimal). This method uses a combination of 4-bit binary codes to represent 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 decimal digits of a decimal number. The most commonly used BCD code is called the 8421BCD code, and 8.4.2.1 is the bit value of the 4-digit binary number.
Convert the decimal number 75.4 to BCD code like:
75.4=(0111 0101.0100)BCD If you convert the BCD code 1000 0101.0101 to a decimal number, such as: (1000 0101.0101) BCD=85.5
Note: The number represented by the same 8-bit binary code is not the same when it is considered to represent a binary number and it is considered to be a binary-coded decimal number.
For example, when it is treated as a binary number, its value is 24; but as a 2-bit BCD code, its value is 18.
For another example, 00011100, (which represents an 8-bit binary number), if it is treated as a binary number, has a value of 28, but cannot be regarded as a BCD code because it is an illegal code in the 8421 BCD code.
The figure on the right is the correspondence table between the decimal number and the 8421BCD code:
The remaining 3 code formed by adding 841 code to 3 is a BCD code, which is formed by adding 841 code to 3 (that is, the remaining 3 codes are based on the 8421 code, each decimal number BCD code plus the binary number 0011 owned). Because there are no 610 to 1111 codes in the 8421 code, there are no 6 codes of 0000~0010 and 1101~1111 in the remaining 3 codes. The remaining 3 yards do not have the right, but have self-complementary, the remaining 3 yards is a kind of "self-complementing code for 9"
8421 code is the name of mainland China.
That is the BCD code. Binary-Coded Decimal, referred to as BCD, is called BCD code or binary-decimal code, also known as binary code decimal number. Is a binary digitally encoded form with a binary coded decimal code. This encoding takes advantage of four bits to store a decimal number, allowing fast conversion between binary and decimal. This coding technique is most commonly used in the design of accounting systems because accounting systems often require accurate calculations of very long strings of numbers. Compared with the general floating-point notation method, the BCD code can save the accuracy of the value and eliminate the time taken for the computer to perform floating-point operations. In addition, BCD coding is also very common for other calculations that require high precision.
Since decimal numbers have 0, 1, 2, ..., and 9 ten digits, at least 4 binary codes are required to represent a 1-digit decimal number. The 4-digit binary code has 2^4=16 code groups. Among the 16 codes, 10 can be selected to represent 10 decimal numbers, for a total of N=16! /(16-10)! Approximately 10 times the ratio of 2.9 times 10 to 10 squares. Commonly used BCD codes are listed at the end.
Conversion of 3 yards to 8421BCD codeThe most commonly used BCD code is represented by a binary code of ten values ​​from "0" to "9". This kind of coding method is called "8421 code" in mainland China. In addition, different coding methods have been developed to meet different needs in response to different needs. These codes can be roughly divided into two types: a right code and an unweight code:
Have the right BCD code, such as: 8421 (most commonly used), 2421, 5421...
No right BCD code, such as: 3 yards, Gray code...
The Yusan code is a self-compensation code for 9 and thus can bring convenience to the operation. Secondly, when the decimal numbers represented by the two remaining three codes are added, the carry signal can be correctly generated, but the sum must be corrected. The method of correction is: if there is a carry, the result is increased by 3; if there is no carry, the result is decremented by 3.
8421BCD code converted to the remaining 3 yardsThrough the WEWB32 software experiment, the logical function of inputting BCD code into the remaining three codes is:
Input ports a, b, c, d, output ports e, f, g, h, denoted by G3, G2, G1, G0:
G3=A'BC+A'BD+ABC'
G2=A'B'C+A'BC'D'+B'C'D
G1=A'C'D'+A'CD+B'C'D'
G0=A'D'+B'C'D'
There are logic functions to draw the logic circuit diagram as follows:
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