The only data that can be recognized in a computer is binary, with a low level representing 0 and a high level representing 1
Symbolic representation of progressions: Binary B, Decimal D, Hexadecimal H
True value: a number that conforms to human convention
machine number: the form in which the number is actually stored inside the machine.The plus and minus signs need to be "digitize“
| 15 —— 1111 | +15 —— 0 1111 |
|---|---|
| 8 —— 1000 | -8 —— 1 1000 |
Representation of data: fixed-point and floating-point numbers
Fixed Points:The position of the decimal point is fixed. Eg: 996.007 - regular counting
Floating point numbers:The position of the decimal point is not fixed. Eg: 9.96007 x 10 x 10 - scientific notation
fixed point
Fixed points are divided intounsigned numbercashlessSigned numbers (original, inverse, complement, shift)
Unsigned numbers: all binary bits throughout the word length of the machine are numeric bits, and the absence of a sign bit corresponds to the absolute value of the number.Usually only unsigned integers, and there are no unsigned decimals.
source code
reverse code
binary code with 0 and 1 interchanged
decode
floating point
Floating point numbers are numbers where the position of the decimal point is not fixed, and they can represent a larger range of numbers.
Floating point numbers are represented in the following table
| ordinal number (e.g. for rainforests) | coding for steps (e.g. decimal or Roman numeral) | numerals | mantissa (i.e. fractional part of common logarithm in math.) |
|---|
In floating-point representations, the ordinal code is usuallysigned plain integerThe digits aresigned decimal。
Floating point numbers are usually expressed as:
$$
N=M*R^E
$$
where M is called the tail number, R is called the base number, and E is called the order code.
coding for steps (e.g. decimal or Roman numeral)which determines the number of floating-point numbers that can be represented by theNumerical range。
mantissa (i.e. fractional part of common logarithm in math.)which determines the number of floating-point numbers that can be represented by thenumerical precision。
Common check digits (non-focused)
parity check code
Parity check is a simple and effective checking method. The basic idea is: by adding a parity bit to the code to make the number of 1's in the code odd (odd parity) or for (even parity), so that the order code becomes 2. For odd parity, it can detect the code with an error in the odd bits of the code, but it cannot find the case of an error in the even bits, i.e., when an error occurs in the odd bits of the legal code, that is, the 1's in the code have become 0's or 0's have become 1's, then the parity of the number of 1's in the code is changed so that the error can be detected.
There are 3 common types of parity codes: horizontal parity, vertical parity, and horizontal-vertical parity.
Heming Code (emphasis added)
Hemming code is composed by inserting k check digits between data bits, and by expanding the order code for error telling and error correction.
Let the data bit be n bits and the check bit be k bits, then n and k must satisfy the following equation
$$
2^k-1≥n+k
$$
cyclic redundancy check digit
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