# The conversion mechanism for binary to decimal is

### How is a binary number converted to decimal number method?

1, integer binary to decimal

Methods: first of all, the binary number to make up the number of digits, the first if the first is 0 on behalf of a positive integer, if the first is 1 on behalf of a negative integer.

If the first is a positive integer of 0, after completing the number of digits, the number of digits in the binary will be multiplied by the corresponding value, and then added together to obtain the decimal system.

If the first digit of a binary number is a 1, you need to invert it and convert it.

2, decimal binary conversion to decimal

Method: the number of bits in binary and the corresponding value of the multiplication, and then added, the value of the converted decimal.

Expanded Information:

Binary is a widely used number system in computing technology. Binary data is a number represented by two digits, 0 and 1. It has a base of 2, a rounding rule of “two into one” and a borrowing rule of “one for two,” discovered by Leibniz, the 18th-century German philosopher of mathematics. The current computer system is basically a binary system, the data in the computer is mainly stored in the form of complementary code. The binary in a computer is a very tiny switch, with ‘on’ for 1 and ‘off’ for 0.

The invention and application of computers in the 20th century, which has been called one of the major symbols of the third technological revolution, was a major success, as digital computers can only recognize and process symbols consisting of ‘0’ . ‘1’ symbol strings consisting of codes. Its mode of operation is precisely binary. 19th century Irish logician George Boole’s process of thinking about logical propositions was transformed into a process of thinking about the symbols ‘0’.””””””. 1”, binary is a system of 2-digit progressions. 0 and 1 are the basic operators. Because it uses only two numeric symbols, 0 and 1, it is very simple and convenient, and easy to realize electronically.

### How are binary numbers converted to decimal numbers?

1, Binary to decimal conversion The value of any binary number is represented by its per-bit weighted expansion.

2, decimal collation converted to binary. Convert the decimal integer into a binary integer using the “divide by 2 to take the inverse of the remainder method”. That is, the decimal integer divided by 2, a quotient and a remainder; then the quotient divided by 2, and a quotient and a remainder; and so on, until the quotient is equal to zero. The inverse of the remainder obtained each time is the number of digits in the corresponding binary number.

3, decimal decimals into binary decimals. Decimal decimal decimal converted to binary decimal is to use the “multiply by 2 to take the integer method”. That is, with 2 to multiply the decimal decimal number one by one, each time the product of the integer part of the respective order of appearance in order to get the corresponding binary decimal number.

4. Binary number to hexadecimal. Binary number into hexadecimal number is the integer part of the binary number from right to left for each group of four, each group of a hexadecimal integer, less than four, in front of the complement of 0; and binary decimal converted to hexadecimal decimal part of the binary decimal part of a group of four, each group of a hexadecimal decimal from left to right.

Expanded

Decimal into R decimal number rotation into R decimal number to be divided into two parts: the integer part of the integer to be divided by R to take the remainder until the quotient is 0, the remainder that is binary digits of the digits, the remainder of the number of digits from right to left (reverse order). Fractional part to be multiplied by R to take the integer, the resulting integer that is the digits of the binary digit, the integer from left to right (sequential arrangement).

Hexadecimal into binary: each hexadecimal number corresponds to four bits of binary, bit by bit expansion.

### What is the law of binary to decimal conversion?

The law of binary to decimal conversion is: from right to left, multiply the number on each bit by the corresponding power of 2, and then add all the products to get the decimal result. For example, the binary number 1011, converted to decimal is: 12^3+02^2+12^1+12^0=8+0+2+1=11.

### How to convert binary to decimal

The law of converting binary to decimal is to multiply the bit-weights in each position of binary by the number of digits in the position, and then add them together, and the result is the corresponding decimal. Bit weight value is some kind of evolution of each position of the data base, such as the decimal system, a bit weight for the zero power of 10, 10 bit power for the 10th power, the rest of the time analogous to the binary system is the same reason. So for example, the decimal of 101101 is 1 * 2 to the 5th power + 0 * 2 to the 4th power + 1 * 2 to the 3rd power + 1 * 2 to the 2nd power + 0 * 2 to the 1st power + 1 * 2 to the 0th power = 45, then 45 is the corresponding decimal number.