How to convert programming between 2,6,8,10,16 decimal systems?

HexadecimalThe conversion between the eggplants isBinary numbers, octal numbers, hexadecimal numbers to decimal numbers.

There is a formula: the digits of binary, octal, and hexadecimal numbers are each given to the power of their respective bases (n-1), and the sum of their sums is the corresponding decimal number. single digit, n=1; Ten digits, n=2 for example:

110b = 1*2 to the 2nd power + 1*2 to the 1st power + 0*2 to the 0th power = 0 + 4 + 2 + 0 = 6d.

110q = 1*8 to the 2nd power + 1*8 to the 1st power + 0*8 to the 0th power = 64 + 8 + 0 = 72d.

The relevance is as follows. Operation.

Addition. Binary addition has four calendar cases: 0+0=0,0+1=1,1+0=1,1+1=10 (0 is rounded to 1).

Multiplication. There are four cases of binary multiplication: 0 0=0, 1 0=0, 0 1=0, 1 1=1.

Subtraction. There are four cases of binary subtraction: 0 0=0, 1 0=1, 1 1=0, and 0 1=1.

Division. There are two cases of binary division (divisor.

Can only be 1): 0 1 = 0, 1 1 = 1.

HexadecimalThe conversion between is as follows:

There is a formula: binary vertical number.

Octadecimal numbers, hexadecimal numbers.

The sum of the digits is the (n-1) power of their respective bases, and the sum of their sums is the corresponding decimal number. single digit, n=1; Ten digits, n = 2.

For example: 110b = 1*2 to the power of 2 to the power of 1*2 to the power of 1 * 2 to the power of 0 * 2 to the power of 0 + 4 + 2 + 0 = 6d.

110q = 1*8 to the 2nd power + 1*8 to the 1st power + 0*8 to the 0th power = 64 + 8 + 0 = 72d.

110h=1*16 to the 2nd power, 1*16 to the 1st power, 0*16 to the 0th power, 256+16+0=272d.

Hexadecimal is the more commonly used programming language.

Because two hexadecimal digits specify exactly one byte. On some platforms, the power of 2, the size of the word, and the instructions are easier to understand. The modern ubiquitous x86 architecture also falls into this category, but octal rarely uses this architecture, although the binary encoding of the opcode for certain properties becomes more obvious, when displayed in octal, such as modrm bytes, which are divided into this fibre and 3 bits, so octal can be used to describe these encodings.

The letter O stands for octal, D for decimal, B for two groups, and H for hexadecimal.

Convert binary numbers to octal numbers: starting from the decimal point, the integer part is to the left, the decimal part is to the right, every 3 digits is a group of 1 octal number representatives, less than 3 digits should be filled with "0" to make up 3 digits, and an octal number is obtained.

Example]: 10001111

So the octal representation of 10001111 is (217)8

Convert binary numbers to hexadecimal numbers: When converting binary numbers to hexadecimal numbers, you only need to start from the decimal point position, divide every four digits of binary to the left or right (less than four digits can be filled with 0), and then write out the hexadecimal number corresponding to each group of binary numbers.

Example]: 10001111

8 f, so the 10001111 of [2] hexadecimal or instructed is expressed as (8f).

Similar to binary conversion bit decimal.

There are usually two ways to convert octal to hexadecimal algorithms:

1. Convert octal to binary first, and then convert binary to hexadecimal.

2. Convert octal to decimal first, and then convert decimal to hexadecimal.

Hexadecimal to binary: The hexadecimal number is divided by 2 to obtain the binary number, each hexadecimal corresponds to four binaries, and the leftmost zero is added when it is insufficient.

Example]: 0x8f8 f

So the binary of 0x8f is 10001111.

There are two ways to convert between octal and hexadecimal:

First, the conversions between them can be converted to binary and then to each other.

Second: The conversions between them can be converted to decimal first and then to each other.

For example, a hexadecimal number 053977, convert it to binary 001 010 011 100 101 110 111, and then convert the pure binary to octal, and the octal is 1234567.

Similar to binary to decimal system.

Each bit converts into three digits: 1-001, 6-110

Join together 001 110, and then remove the previous 0 to get 1110, which is the converted binary number.

Small decimal to binary.

Multiply the decimal by 2, then take out the integer part of the product, continue to multiply the remaining decimal part by 2, then take out the integer part of the product, and so on until the decimal part of the product is zero, at which point 0 or 1 is the last digit of binary. or until the required accuracy is achieved.

Then arrange the integer parts in order, the integer taken first is used as the high significant digit of the binary decimal place, and the integer taken later is taken as the low significant digit.

The answer is to calculate -12 64=

Then multiply by two to round up to binary, take 0, take 0, take 1, take 1, and add it up.

The following infiltration staking steps can be used to convert decimal 10 to hexadecimal:

Divide the decimal number cluster by 16 to get the quotient and remainder.

2.Divide the quotient by 16 to get the new quotient and remainder.

3.Repeat the above steps until the quotient is 0, and then arrange the remainders from the bottom to the top to get the hexadecimal representation.

Thus the hexadecimal representation of 258 is 102:258 16=16 with a remainder of 2; 16 16 = 1 with a remainder of 0.