Primary, inverse, and complement of decimals
Converted to binary is the integer part divided by two to make 1
Decimal part multiplied by two until it becomes 1
Significant bit 0 means positive and 1 negative
Positive: primary = complement
Negative:
Primary
=
Positive part (with negative sign removed) of binary value and sign bit (leftmost bit) is 1
Inverse
=
Positive part ( minus sign removed) and the sign bit (leftmost bit) is 1
Inverse code
=
Binary value of the positive part (minus sign removed), inverted by bit
Complement code
=
Inverse code
+
1
Decimal point is still in point
Fixedpoint numbers
The socalled fixedpoint numbers are numbers in which the position of the decimal point is fixed. In computers, fixedpoint numbers are often used to represent integers and pure decimals, called fixedpoint integers and fixedpoint decimals, respectively.
Fixedpoint integer: The highest binary digit of a number is the number sign bit, which is used to represent the sign of the number; while the decimal point’s position is defaulted to be after the lowest (i.e., rightmost) binary digit, but the decimal point does not take up a separate binary digit, as follows:
0
1001010010001010001
Number sign bit
Numerical bit
Numerical bit
Numerical bit
Numerical bit
Numerical bit
Number sign bit
Numeric bits
Decimal bits
So, in a fixedpoint integer, all the binary bits to the right of the number sign bit represent an integer value.
Fixedpoint decimals: The highest binary digit of a number is the number sign bit, which is used to represent the sign of the number; the decimal point is positioned after the number sign bit by default, and does not take up a separate binary digit, as shown here:
0
1001010010001010001
Number Sign BitDecimal Bit
Value Bit
Thus, in a fixedpoint decimal, all the binary digits to the right of the number sign bit represent a pure decimal.
2. Floatingpoint numbers
In computers, fixedpoint numbers are usually used to represent only integers or pure decimals. Numbers that have both an integer and a decimal part are usually represented as floating point numbers because the decimal point is not in a fixed position.
Floatingpoint numbers, as they are called in computers, are numbers in which the position of the decimal point is not fixed. Generally, a decimal number D with both integer and decimal parts can be expressed in the following form:
D=R*10N
Where R is a pure decimal number and N is an integer.
Such as a decimal number 123.456 can be expressed as: 0.123456 * 103, decimal decimal decimal 0.00123456 can be expressed as 0.123456 * 102. pure decimal R, the first digit after the decimal point is generally nonzero numbers.
Similarly, for binary numbers that have both integer and decimal parts, the mouth can also be expressed in the following form:
D = R*2N
Where R is a binary fixedpoint decimal, known as the trailing digit of D; N is a binary fixedpoint integer, known as the ordinal code of D, which reflects the actual position of the decimal point of the binary number D. In order to represent the maximum number of digits in a finite number of binary digits, the first digit after the decimal point (i.e., one bit after the sign bit) of a fixedpoint decimal R is generally a nonzero digit (i.e., a “1”).
In computers, a string of consecutive binary bits is usually used to store a binary floatingpoint number, whose general structure is shown in the following diagram:
Ordinal symbol
N
Numeric symbol
R

Ordinal code section

Decimal bits
Trailing number section
how to calculate the negative decimal original code, complement, inverse code and shift code, such as (0.3125) decimal
The first decimal point indicates positive or negative, negative 1, first regardless of positive or negative, the integer part is 0 do not have to seek, the decimal part of the 0.3125 * 2 = 0.625, the integer part of the 0, the second decimal point is 0, and then calculate the 0.625 * 2 = 1.1.25, the integer part is 1, the second digit after the decimal point is 1, remove the integer 1,0.25*2=0.5, the integer part is 0, the third digit is 0,0.5.*2=1, the last digit is 1, the original code (1.0101). (Check that 2^2+2^4=0.25+0.0625=0.3125). For negative numbers, the inverse code is the original code inverted (1.1010), and for negative numbers, the complement is the original code inverted + 1 (1.1011), and there is no shift code for decimals.