Convert the following binary numbers to hexadecimal. i. 10010011 ii. 10110111
The Correct Answer and Explanation is :
To convert binary numbers to hexadecimal, we can follow a systematic approach. Let’s convert the given binary numbers (10010011) and (10110111) step by step.
Step 1: Understanding Binary and Hexadecimal
Binary is a base-2 number system that uses only two digits: 0 and 1. Each digit represents a power of 2. For example, the binary number (10010011) can be interpreted as follows:
- (1 \times 2^7) (128)
- (0 \times 2^6) (0)
- (0 \times 2^5) (0)
- (1 \times 2^4) (16)
- (0 \times 2^3) (0)
- (0 \times 2^2) (0)
- (1 \times 2^1) (2)
- (1 \times 2^0) (1)
Adding these values together: (128 + 16 + 2 + 1 = 147).
Hexadecimal is a base-16 number system that uses sixteen distinct symbols: 0-9 and A-F, where A through F represent the values 10 to 15, respectively. Each hexadecimal digit represents a power of 16.
Step 2: Converting Binary to Hexadecimal
- Binary Number: (10010011)
- We group the binary digits into pairs from the right (add leading zeros if necessary):
- (1001 0011)
- Convert each group to hexadecimal:
- (1001) (binary) = (9) (hexadecimal)
- (0011) (binary) = (3) (hexadecimal)
- Therefore, (10010011) in hexadecimal is 93.
- Binary Number: (10110111)
- Again, group the binary digits:
- (1011 0111)
- Convert each group to hexadecimal:
- (1011) (binary) = (B) (hexadecimal)
- (0111) (binary) = (7) (hexadecimal)
- Therefore, (10110111) in hexadecimal is B7.
Conclusion
- The hexadecimal representation of the binary number (10010011) is 93.
- The hexadecimal representation of the binary number (10110111) is B7.
This conversion process highlights the relationship between different number systems and the ease of converting from binary to hexadecimal using grouping and conversion techniques. Understanding these principles is essential for working with digital systems and programming, where binary and hexadecimal are commonly used.