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AQA GCSE · Question 01.3 · Fundamentals of data representation
State the largest decimal number that can be represented using 6 bits.
State the largest decimal number that can be represented using 6 bits.
How to approach this question
The largest number that can be represented with a certain number of bits is when all bits are set to 1.
1. For 6 bits, this would be the binary number 111111.
2. You can calculate this in two ways:
a) Sum the place values: 32 + 16 + 8 + 4 + 2 + 1 = 63.
b) Use the formula 2^n - 1, where n is the number of bits. So, 2^6 - 1 = 64 - 1 = 63.
Full Answer
63
The largest decimal number that can be represented with 'n' bits is calculated using the formula 2^n - 1. This is because the range of numbers starts from 0.
In this case, n = 6.
So, the largest number is 2^6 - 1.
2^6 = 64.
64 - 1 = 63.
Alternatively, you can find the decimal value of the largest 6-bit binary number, which is 111111.
The place values are 32, 16, 8, 4, 2, 1.
Adding these together: 32 + 16 + 8 + 4 + 2 + 1 = 63.
Common mistakes
✗ Giving the answer 64 (which is 2^6, the total number of possible values, not the largest value).
✗ Calculating 2^n instead of 2^n - 1.
✗ Incorrectly calculating 2^6.
Practice the full AQA GCSE Computer Science Paper 2
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