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West Midlands | 26 March SDC | Iswat Bello | Sprint 1 | Number systems #370

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Complete answers for number systems exercises in README.md
Iswanna Mar 13, 2026
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docs: clarify method to test if a binary number is a power of two
Iswanna Mar 14, 2026
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Clarify and expand answers in README.md
Iswanna Mar 27, 2026
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40 changes: 20 additions & 20 deletions number-systems/README.md
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Expand Up @@ -5,61 +5,61 @@ Do not convert any binary numbers to decimal when solving a question unless the
The goal of these exercises is for you to gain an intuition for binary numbers. Using tools to solve the problems defeats the point.

Convert the decimal number 14 to binary.
Answer:
Answer: 1110

Convert the binary number 101101 to decimal:
Answer:
Answer: 45

Which is larger: 1000 or 0111?
Answer:
Answer: 1000

Which is larger: 00100 or 01011?
Answer:
Answer: 01011

What is 10101 + 01010?
Answer:
Answer: 11111

What is 10001 + 10001?
Answer:
Answer: 100010

What's the largest number you can store with 4 bits, if you want to be able to represent the number 0?
Answer:
Answer: 15

How many bits would you need in order to store the numbers between 0 and 255 inclusive?
Answer:
Answer: 8 bits

How many bits would you need in order to store the numbers between 0 and 3 inclusive?
Answer:
Answer: 2 bits

How many bits would you need in order to store the numbers between 0 and 1000 inclusive?
Answer:
Answer: 10 bits
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@Iswanna Iswanna Mar 27, 2026

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I have compared my answer with the answer in the reference material, and I can see that the provided answer is more detailed. It correctly notes that 10 bits provide 1,024 combinations, leaving 23 spare values after storing the range 0–1000 (which contains 1,001 total values). I will update my answer to include this context.


How can you test if a binary number is a power of two (e.g. 1, 2, 4, 8, 16, ...)?
Answer:
Answer: It can be tested if one of the bits in the value is one e.g 0100, 10, 100
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@Iswanna Iswanna Mar 27, 2026

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I also see here that my answer was not precise enough. Stating that ‘one of the bits in the value is one' could incorrectly include numbers like 3 (0011) or 6 (0110), which are not powers of two. I have updated the answer to specify that there must be exactly one bit set to 1.


Convert the decimal number 14 to hex.
Answer:
Answer: E

Convert the decimal number 386 to hex.
Answer:
Answer: 182

Convert the hex number 386 to decimal.
Answer:
Answer: 902

Convert the hex number B to decimal.
Answer:
Answer: 11

If reading the byte 0x21 as a number, what decimal number would it mean?
Answer:
Answer: 33

If reading the byte 0x21 as an ASCII character, what character would it mean?
Answer:
Answer: !

If reading the byte 0x21 as a greyscale colour, as described in "Approaches for Representing Colors and Images", what colour would it mean?
Answer:
Answer: very dark gray
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@Iswanna Iswanna Mar 27, 2026

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I used 'very dark grey' because 0x21 (decimal 33) is quite close to 0 (black). However, I will update my answer to 'Dark grey' to maintain consistency with the reference material.

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@cjyuan cjyuan Mar 27, 2026

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They mean the same thing. There is no standard for "dark" or "very dark".


If reading the bytes 0xAA00FF as an RGB colour, as described in "Approaches for Representing Colors and Images", what colour would it mean?
Answer:
Answer: purple

If reading the bytes 0xAA00FF as a sequence of three one-byte decimal numbers, what decimal numbers would they be?
Answer:
Answer: 170, 0, 255
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