# hexadecimal to decimal decimal point (computing)

### Hexadecimal with decimals converted to decimal

is directly convertible to

decimal

Example: 126.398H

Integer portion of 126

Hundredths digit:

1 x 16 x 16

(square of 16)

Tenth place:

2×16

(Square of 16 to the first power)

Single digit:

6

(Square of 16 to the zeroth power)

Decimal part 398

3×(16×-1)

9×(16×-2)

8×(16×-3)

Bit 0 of a hexadecimal number has a weight of 0 to the power of 16, bit 1 has a weight of 1 to the power of 16, and bit 2 has a weight of 2 to the power of 16. …… So, at the Nth (N starting from 0) bit, if it’s is the number X (X is greater than or equal to 0, and X is less than or equal to 15, i.e.: F) represents a size of X*16 to the Nth power.

Example: 2AF5 converted to decimal:

Direct calculation is, 5*16^0+F*16^1+A*16^2+2*16^3=10997.

Hexadecimal (English name: Hexadecimal), is a method of representing data in computers. It is different from the representation in our daily life. It consists of 0-9, A-F, and the letters are not case sensitive. Correspondence with the decimal system is: 0-9 corresponds to 0-9; A-F corresponds to 10-15; the number of N can be expressed in 0 ~ (N-1), more than 9 with the letters A-F.

### How to convert hexadecimal to decimal?

The specific algorithm for converting hexadecimal to decimal is:

1. First understand that the hexadecimal number (counting from right to left is the 0th, 1st, and 2nd ……) has the weight of the 0th digit as the 0th power of 16, the 1st digit as the 1st power of 16, the 2nd digit as the 2nd power of 16 and so on in this order.

2, understand that ABCDEF said the binary digits are 10, 11, 12, 13, 14, 15.

3, hexadecimal into decimal formula is: to be from right to left with the binary of each number to multiply by the corresponding square of 16, and then these numbers are added.

Example 1:

2AF5 converted to decimal:

Bit 0: 5 * 16 ^ 0 = 5

Bit 1: F * 16 ^ 1 = 15 * 16 ^ 1 = 240

Bit 2: A * 16 ^ 2 = 10 * 16 ^ 2 = 2560

Bit 3: 2 * 16 ^ 3 = 8192 knot

The result is: 5*16^0+15*16^1+10*16^2+2*16^3=10997

Example 2: CE converted to decimal:

Bit 0: E*16^0=14*16^0=14

Bit 1: C*16^1=12*16^1=192

The result is: 14*16^0+12*16^1=206

Theory of Conversion

1. Conversion of Binary and Hexadecimal Numbers to Decimal:

Using the Expansion by Weights method to convert an arbitrary R-ary number anan-1…. .a1a0.a-1a-2… .a-m into a decimal number whose decimal value is the sum of the product of each digit and its bitwise power.

an×Rn+an-1×Rn-1+…+a1×R1+a0×R0+a-1×R-1+a-2×R-2+…+a-m×R-m

2, decimal converted to 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 of the binary digits, the remainder of the digits from right to left (reverse order). Fractional part to multiply R to get the integer, the integer that is binary digits, integers from left to right (sequential).

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

4, binary into hexadecimal: the binary number from the decimal point to the left (for binary integers) or to the right (for binary decimals) every four bits to form a group, less than four complementary zero.

Multiply a decimal decimal by 16 to get the product, then take out the integer bits, then multiply the decimal portion by 16, and cycle through the operation until the decimal places are 0, or until you get the decimal precision you think is appropriate. Then you concatenate the integers, and that’s the hexadecimal number of decimals you want to convert.

Expanded information:

Converting hexadecimal numbers to decimal numbers

In hexadecimal 2, two Arabic numbers are used: 0 and 1;

In hexadecimal 8, eight Arabic numbers are used: 0, 1, 2, 3, 4, 5, 6, and 7;

In hexadecimal 10, ten Arabic numbers are used: 0 through 9;

Hexadecimal, with sixteen Arabic numerals …… etc… Indians only invented 10 numbers huh?

Hexadecimal is every 16 into 1, but we only have 0 to 9 the ten numbers, so we use A, B, C, D, E, F the six letters to represent 10, 11, 12, 13, 14, 15 respectively. letters are not case-sensitive.