Binary Number Conversion Explanation
How do we convert a binary number to decimal?
In binary representation, each digit represents a power of 2. Starting from the rightmost digit, the powers of 2 increase from 0 to n, where n is the number of digits.
How do we convert a decimal number to binary?
We find the largest power of 2 that is less than or equal to the given number. We write a 1 in the corresponding position and subtract that power of 2 from the original number. We continue this process for the remaining powers of 2 until we reach 2^0.
Binary to Decimal Conversion
To convert a binary number (100011) to decimal, we calculate the value of each digit based on its position. Starting from the rightmost digit, we have 1, 0, 0, 0, 1, and 1. The rightmost digit represents 2^0 (which is 1), the next digit represents 2^1 (which is 2), and so on. We add up these values: 1 + 0 + 0 + 0 + 16 + 32 = 35. Therefore, the binary number (100011) is equal to the decimal number 35.
Decimal to Binary Conversion
To convert the decimal number (64) to binary, we find the largest power of 2 that is less than or equal to the given number. In this case, it is 2^6, which equals 64. We write a 1 in the corresponding position and subtract 64 from the original number. The remaining value is 0. Then, we move to the next smaller power of 2, which is 2^5 (32). Since the remaining value (0) is smaller than 32, we write a 0 in that position. We continue this process for the remaining powers of 2 until we reach 2^0. The resulting binary representation is 1000000.
Understanding how to convert between binary and decimal numbers is an essential skill in the field of computer science and digital electronics. The conversion process involves understanding the positional value of each digit in the number representation.
When converting a binary number to decimal, we calculate the value by multiplying each digit by the corresponding power of 2 and summing up the results. This process helps us understand the equivalence between binary and decimal numbers.
On the other hand, converting a decimal number to binary requires identifying the largest power of 2 that fits into the given number, writing a 1 in that position, and subtracting the value. We continue this process for each decreasing power of 2 until we reach 2^0, resulting in the binary representation of the decimal number.
By mastering these conversion techniques, you can develop a solid foundation in understanding number systems and their applications in various fields. Practice converting different numbers to deepen your comprehension and enhance your problem-solving skills.