Advanced Placement (AP) Computer Science

What is the first step to convert a binary number to hexadecimal?

1. Convert each binary digit to decimal

2. Split the binary number into groups of four bits

3. Multiply each bit by a power of two

4. Add all groups together

The correct answer is: Split the binary number into groups of four bits

The process of converting a binary number to hexadecimal begins by splitting the binary number into groups of four bits. This is because each hexadecimal digit corresponds to a four-bit binary group, as hexadecimal is a base-16 numbering system and binary is base-2. By organizing the binary number into these four-digit segments, each segment can then be easily mapped to its equivalent hexadecimal digit. This approach simplifies the conversion process, allowing you to systematically translate the binary representation to hexadecimal without needing to perform additional calculations like powers of two or decimal conversions at this stage. Understanding this grouping is vital for efficient conversion, as it lays the foundation for the subsequent steps where each group of four binary digits can be directly associated with a hexadecimal character, significantly speeding up the conversion process.