The binary value of the ASCII letter “c” is 0110 0011. Using the handy chart that we learned in the lesson, convert this number to its decimal value. You’ll need to use some math for this question.
The Correct Answer and Explanation is :
The correct answer is: 99
To convert the binary value of the ASCII letter “c” (0110 0011) to its decimal equivalent, we need to understand the binary numbering system and how to interpret each bit’s contribution to the overall value.
In binary, each digit represents a power of 2, starting from the rightmost digit (which represents (2^0)) to the leftmost digit (which represents (2^n), where (n) is the position from the right starting at 0). The binary number 0110 0011 can be broken down as follows:
- The binary representation is:
- 0 (2^7)
- 1 (2^6)
- 1 (2^5)
- 0 (2^4)
- 0 (2^3)
- 0 (2^2)
- 1 (2^1)
- 1 (2^0)
Now, we can calculate the decimal value by adding the contributions of the bits that are set to 1:
- The leftmost bit (0) contributes (0 \times 2^7 = 0)
- The next bit (1) contributes (1 \times 2^6 = 64)
- The next bit (1) contributes (1 \times 2^5 = 32)
- The next bit (0) contributes (0 \times 2^4 = 0)
- The next bit (0) contributes (0 \times 2^3 = 0)
- The next bit (0) contributes (0 \times 2^2 = 0)
- The next bit (1) contributes (1 \times 2^1 = 2)
- The rightmost bit (1) contributes (1 \times 2^0 = 1)
Now, we sum all these contributions together:
[
0 + 64 + 32 + 0 + 0 + 0 + 2 + 1 = 99
]
Thus, the decimal value of the binary number 0110 0011 is 99.
This process illustrates how binary numbers represent values in a way that computers can process. By understanding the powers of 2 and how to interpret the binary representation, we can convert binary to decimal effectively. This method of conversion is essential in computing and programming, as it allows us to understand how characters and data are stored and manipulated at the most basic level.