AQA GCSE · Question 01.2 · Fundamentals of data representation
Convert the binary number 10111001 into hexadecimal. You should show your working.
How to approach this question
1. Take the 8-bit binary number 10111001.
2. Split it into two 4-bit groups (nibbles): 1011 and 1001.
3. Convert each nibble into its decimal equivalent. The place values for a nibble are 8, 4, 2, 1.
4. For 1011: (1*8) + (0*4) + (1*2) + (1*1) = 8 + 0 + 2 + 1 = 11.
5. For 1001: (1*8) + (0*4) + (0*2) + (1*1) = 8 + 0 + 0 + 1 = 9.
6. Convert the decimal values to their hexadecimal equivalents. Decimal 1-9 are the same in hex. Decimal 10-15 are A-F. So, 11 becomes B and 9 remains 9.
7. Combine the two hex digits to get the final answer.
Full Answer
To convert binary to hexadecimal, you group the binary digits into sets of four (called nibbles), starting from the right.
1. The binary number is 10111001.
2. Split into two nibbles: `1011` and `1001`.
3. Convert the first nibble `1011`: The place values are 8, 4, 2, 1. So, (1*8) + (0*4) + (1*2) + (1*1) = 11. The decimal number 11 is represented by the character 'B' in hexadecimal.
4. Convert the second nibble `1001`: The place values are 8, 4, 2, 1. So, (1*8) + (0*4) + (0*2) + (1*1) = 9. The decimal number 9 is represented by '9' in hexadecimal.
5. Combine the results to get the hexadecimal number: B9.
Common mistakes
✗ Not splitting the binary number into nibbles.
✗ Splitting into incorrect group sizes (e.g., groups of 3).
✗ Making an error when converting a nibble to decimal.
✗ Forgetting that decimal 10-15 are represented by letters A-F in hexadecimal.
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