Convert the binary 010101 to decimal
The Correct Answer and Explanation is:
To convert the binary number 010101 to decimal, we follow the principles of binary-to-decimal conversion. In the binary number system, each digit (bit) represents a power of 2, starting from the rightmost digit, which is (2^0).
Step-by-Step Conversion
- Identify Each Bit’s Position:
- The binary number 010101 has six bits.
- From right to left, the positions are as follows:
- (2^5) (for the first bit, which is 0)
- (2^4) (for the second bit, which is 1)
- (2^3) (for the third bit, which is 0)
- (2^2) (for the fourth bit, which is 1)
- (2^1) (for the fifth bit, which is 0)
- (2^0) (for the sixth bit, which is 1)
- Calculate Each Bit’s Value:
- For the bit values:
- (0 \times 2^5 = 0)
- (1 \times 2^4 = 16)
- (0 \times 2^3 = 0)
- (1 \times 2^2 = 4)
- (0 \times 2^1 = 0)
- (1 \times 2^0 = 1)
- Add Up the Values:
- Now, sum the values from the active bits (where the bit is 1):
- (0 + 16 + 0 + 4 + 0 + 1 = 21)
Final Answer
Thus, the binary number 010101 converts to the decimal number 21.
Explanation of the Binary System
Binary is a base-2 numeral system, which uses only two symbols: 0 and 1. Each position in a binary number corresponds to an increasing power of 2, just as each position in the decimal system corresponds to a power of 10. This binary system is fundamental in computing and digital electronics, as it aligns with the on/off states of electrical signals.
In practice, converting from binary to decimal involves identifying which bits are set (1s) and calculating their contribution to the total decimal value. The simplicity of the binary system is what makes it efficient for computer processing, enabling rapid calculations and data storage using the most basic form of digital representation. Understanding this conversion process is essential for anyone working in fields related to computer science or digital systems.