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AQA GCSE · Question 01.1 · Fundamentals of data representation
Convert the binary number 11010100 into decimal.
Convert the binary number 11010100 into decimal.
How to approach this question
To convert a binary number to decimal, you need to use place values which are powers of 2.
1. Write down the binary number: 11010100.
2. Above each digit, write its corresponding place value, starting from the right with 2^0 (1), then 2^1 (2), 2^2 (4), and so on.
128 64 32 16 8 4 2 1
1 1 0 1 0 1 0 0
3. Add up the place values where the binary digit is 1.
4. The sum is 128 + 64 + 16 + 4.
5. Calculate the final sum: 128 + 64 = 192, 192 + 16 = 208, 208 + 4 = 212.
Full Answer
212
Binary numbers are read from right to left, with the rightmost digit being the least significant bit. The place values are powers of 2. For an 8-bit number like 11010100, the place values are:
- 1 * 2^7 = 128
- 1 * 2^6 = 64
- 0 * 2^5 = 0
- 1 * 2^4 = 16
- 0 * 2^3 = 0
- 1 * 2^2 = 4
- 0 * 2^1 = 0
- 0 * 2^0 = 0
Adding these values together gives: 128 + 64 + 0 + 16 + 0 + 4 + 0 + 0 = 212.
Common mistakes
✗ Starting place values from the left instead of the right.
✗ Calculating powers of 2 incorrectly (e.g., 2^3 = 6 instead of 8).
✗ Including place values where the binary digit is 0 in the sum.
Practice the full AQA GCSE Computer Science Paper 2
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