In your study of computer science, you have probably been exposed in one way or another to the idea of a binary number. Binary representation is important in computer science since all values stored within a computer exist as a string of binary digits, a string of 0s and 1s. Without the ability to convert back and forth between common representations and binary numbers, we would need to interact with computers in very awkward ways. Show Integer values are common data items. They are used in computer programs and computation all the time. We learn about them in math class and of course represent them using the decimal number system, or base 10. The decimal number 23310233_{10} and its corresponding binary equivalent 11 101001211101001_2 are interpreted respectively as 2×102+3×101+3×100 2\times10^{2} + 3\times10^{1} + 3\times10^{0} and 1×27+1×26+1×25+0×24 +1×23+0×22+0×21+1×20 1\times2^{7} + 1\times2^{6} + 1\times2^{5} + 0\times2^{4} + 1\times2^{3} + 0\times2^{2} + 0\times2^{1} + 1\times2^{0} But how can we easily convert integer values into binary numbers? The answer is an algorithm called “Divide by 2” that uses a stack to keep track of the digits for the binary result. The Divide by 2 algorithm assumes that we start with an integer greater than 0. A simple iteration then continually divides the decimal number by 2 and keeps track of the remainder. The first division by 2 gives information as to whether the value is even or odd. An even value will have a remainder of 0. It will have the digit 0 in the ones place. An odd value will have a remainder of 1 and will have the digit 1 in the ones place. We think about building our binary number as a sequence of digits; the first remainder we compute will actually be the last digit in the sequence. As shown below, we again see the reversal property that signals that a stack is likely to be the appropriate data structure for solving the problem. Decimal-to-binary conversionThe Python code below implements the Divide by 2 algorithm. The function
The algorithm for binary conversion can easily be extended to perform the conversion for any base. In computer science it is common to use a number of different encodings. The most common of these are binary, octal (base 8), and hexadecimal (base 16). The decimal number 233233 and its corresponding octal and hexadecimal equivalents 3518351_{8} and E 916E9_{16} are interpreted as 3×82+5×81+1×80 3\times8^{2} + 5\times8^{1} + 1\times8^{0} and 14×161+9×160 14\times16^{1} + 9\times16^{0} The function
A solution to this problem is to extend the digit set to include some alphabet characters. For example, hexadecimal uses the ten decimal digits along with the first six alphabet characters for the 16 digits. To implement this, a digit string is created that stores the digits in their corresponding positions. 0 is at position 0, 1 is at position 1, A is at position 10, B is at position 11, and so on. When a remainder is removed from the stack, it can be used to index into the digit string and the correct resulting digit can be appended to the answer. For example, if the remainder 13 is removed from the stack, the digit D is appended to the resulting string. How do you convert a number to a different base in Python?In Python, you can simply use the bin() function to convert from a decimal value to its corresponding binary value. And similarly, the int() function to convert a binary to its decimal value. The int() function takes as second argument the base of the number to be converted, which is 2 in case of binary numbers.
How do you convert a number from one base to another base?Decimal to Other Base System
Step 1 − Divide the decimal number to be converted by the value of the new base. Step 2 − Get the remainder from Step 1 as the rightmost digit (least significant digit) of new base number. Step 3 − Divide the quotient of the previous divide by the new base.
How do you convert base 2 to base 10 in python?Convert a binary number(base 2) to the integer(base 10) in Python. Syntax: int(x = binary_string,base = 2) .. Parameters: x = binary string(can be hexadecimal, octal), base = the base of the string literal.. Returns: Integer form of the binary string representation.. How do you convert to base 2 in Python?Use bin() Function to Convert Int to Binary in Python
In Python, you can use a built-in function, bin() to convert an integer to binary. The bin() function takes an integer as its parameter and returns its equivalent binary string prefixed with 0b .
|