How to convert a binary number to hexadecimal?
Converting a binary number to hexadecimal is similar to converting a binary number to octal, except that four bits are combined into one.
E.g. Convert 10111101010.010001B to hexadecimal.
Taking the decimal point as the base, for the integer part, from right to left, a group of four bits, less than four bits in front of a complement of 0. The integer part has 11 bits, divided into three groups, in front of a complement of 0.
For the fractional part, from left to right, a group of four bits, less than four bits behind a complement of 0. The fractional part has 6 bits, divided into two groups, behind a complement of two zeros.
And then each of these groups of four binary digits into a hexadecimal number. The conversion method can be referred to in Table 2-2, or you can use the weighted expansion method for conversion. (Note: If the number obtained after expanding by weights is a number between 0 and 9, it is enough to write this number directly; if it is a number between 10 and 15, it has to be converted to hexadecimal A~F. Pay attention to the correspondence between decimal 10~15 and hexadecimal A~F.)
Result after grouping: 010111101010.01000100B
Result after converting to octal: 5EA.44H
Note: B is the symbol for binary, and after converting to hexadecimal, you should write hexadecimal symbol H.
Extended information:
How to convert binary to hexadecimal?
Method to convert binary number to hexadecimal number:
One binary number can have two states 0 or 1, one hexadecimal number has 16 states 0~9, A, B, C, D, E, F. That is to say, 4 bits of binary are combined together in order to fully express one hexadecimal number, 24=16!
Simply put, one hexadecimal number equals to 4 binary In short, a hexadecimal number is equivalent to a 4-bit binary number. Let’s look at how a 4-bit binary number is converted to a hexadecimal number, and then expand on the conversion of more than 4 bits of binary to hexadecimal.
1, 4-bit binary number is converted to a hexadecimal number
Methods: the 4-bit binary number according to the form of the power to expand the sum, you can.
Example: the 4-bit binary number 1010 converted to a hexadecimal number
Binary number 1010 by the weighted form of the expansion of the form is as follows:
(1010)2 = 1 × 23 + 0 × 22 + 1 × 21 + 0 × 20 = (8 + 0 + 2 + 0)10 = (10)10 = (0A)16
The results are: ( 1101)2=(0A)16
Example: Converting a 4-digit binary number 1001 to a one-digit hexadecimal number
(1001)2=1×23+0×22+0×21+1×20=(8+0+0+1)10=(9)10=(9)16
Results in: (1001)2=(9)16
< p>Observing the last two examples:
(1010)2=(8+0+2+0)10
(1001)2=(8+0+0+1)10
It can be seen that: the 4-bit binary expansion by weights adds up to the sum of the powers corresponding to the bit 1 actually.
Such as binary 1010 only the fourth bit, the second bit is 1, respectively, corresponding to the power of 23 = 8, 21 = 2.
The (1010)2 = (8 + 0 + 2 + 0)10 form of the simplified form as follows:
(1010)2 = (8 + 2)10 = (10)10
(1001)2 = (8 + 1)10 = (9)10
(1001)2 = (8 + 1)10 = (9)10
(1001)2 = (8 + 1)10
(1001)2 = (8 + 1)10 = (9)10 (9)10
Further observation of the above two equations shows that when a certain power occurs in an additive number, its corresponding binary digit must be 1.
Now we get an easier way of converting binary to hexadecimal:
Steps:
1. First, find out the bit of 1 in the 4 bits of the binary, and then write down its corresponding power.
②.Write these weights in the form of summing and summing, and just find the sum.
An example to deepen your understanding
Example (0100) 2-bit hexadecimal number
Steps:
①.First, find out the bit that is 1 in the 4-bit binary number, and then write its corresponding weight. Binary number 0100, the third bit is 1, the weight of 22 = 4
②, the right to write this form of sum, because there is only one right, that is, an addition, we do not need to write the form of addition and sum, the right is the result, that is, (0100) 2 = (4) 10 = (4) 16
Results of (0100) 2 = (4) 16
2, More than 4 binary digits converted to hexadecimal
Methods: more than 4 binary digits, from “right to left”, 4 binary form a part of the shortfall with 0 to fill in, and then converted to a 4-bit binary hexadecimal method of solving.
Example: binary number 10011010 converted to hexadecimal
Binary number 1001101 from right to left, 4 bits for a part of the form is as follows:
01001101
① ② (for the sake of convenience, I left the two parts of the left mark, respectively, to find the solution to each part of)
① (0100) 2=(4)10=(0A)16
②(1101)2=(8+4+1)10=(13)10=(0D)16
Results in (1001101)2=(0AD)16
Binary is a number system that is widely used in computational technology. Binary data is a number represented by two digits, 0 and 1. Its base is 2, and the rule of rounding is “two into one”, and the rule of borrowing is “borrowing one as two”, which was discovered by Leibniz, the 18th-century German master of mathematical philosophy. 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 2-digit system. 0 and 1 are the basic operators. Because it only uses 0, 1 two digital symbols, very simple and convenient, easy to realize electronically.
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, 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 binary to hexadecimal?
(56) How to convert binary to hex 😭😭😭😭😭
How is binary converted to hexadecimal?
Generally, any binary N, can be expressed as N = 2j × S; where J is the binary number, called the order code; J if there is a plus or minus sign, the plus or minus sign is called the order sign; S is a pure decimal, called the number of tails; the number sign, refers to the sign of the whole number of N.
The binary “00101000” can be directly converted to hexadecimal “28”. Byte is the basic storage unit in the computer, according to the different computer word length, the word has a different number of bits, the word length of modern computers is generally 32-bit, that is to say, the number of bits in a word is 32.
The byte is an 8-bit unit of data, a byte can be expressed as a decimal data from 0 to 255. For modern computers with 32-bit word lengths, a word is equal to 4 bytes, and for early 16-bit computers, a word is equal to 2 bytes.
Extended information:
Divide a given decimal integer by base 2, and the remainder is the lowest bit of the binary equivalent. The quotient from the previous step is then divided by base 2, and the remainder is the second lowest bit of the equivalent binary number, until the final resulting quotient equals zero.
The remainder of each division is the number of binary digits, with the last remainder being the highest. Binary from the lowest bit every three bits to convert to decimal that is its corresponding octal. If there are less than three digits in the high digit, zero will be added. Similarly, every four bits of binary from the lowest bit is converted to decimal, which is its corresponding hexadecimal.
How to convert binary to hexadecimal?
Binary to hexadecimal
To convert a binary number to hexadecimal, it is a 4-bit segment, respectively, to hexadecimal.
From right to left 4-bit everything
For example, 100111110110101
Left side of the less than 4-bit can be filled with 0 0100,1111,1011,01012
Element 0000 corresponds to the 16-bit hex 0
0001>>>1
0011>>>3
0100>>>4
0101>>>5
0110>>>6
0111>>6
0111>>7
The number of digits in a code is the same as the number of digits in a code. >>7
1000>>>8
1001>>>9
1010>>>>A
1011>>>B
1100>>>C
1101>>>D
1110>>>E
1111>>>F
So the above binary to hexadecimal is 4FB5