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London | 28-SDC-July | Boshra Mahmoudi | Sprint 1 | Number systems #622

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30 changes: 15 additions & 15 deletions number-systems/Part-1.md
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Expand Up @@ -7,48 +7,48 @@ The goal of these exercises is for you to gain an intuition for binary numbers.
The answers to these questions should be a number, either in binary, hex, or decimal.

Q1: Convert the decimal number 14 to binary.
Answer:
Answer: 1110

Q2: Convert the binary number 101101 to decimal:
Answer:
Answer: 45

Q3: Which is larger: 1000 or 0111?
Answer:
Answer: 1000

Q4: Which is larger: 00100 or 01011?
Answer:
Answer: 01011

Q5: What is 10101 + 01010?
Answer:
Answer: 11111

Q6: What is 10001 + 10001?
Answer:
Answer: 100010

Q7: 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

Q8: How many bits would you need in order to store the numbers between 0 and 255 inclusive?
Answer:
Answer: 8

Q9: How many bits would you need in order to store the numbers between 0 and 3 inclusive?
Answer:
Answer: 2

Q10: How many bits would you need in order to store the numbers between 0 and 1000 inclusive?
Answer:
Answer: 10

Q11: Convert the decimal number 14 to hex.
Answer:
Answer: E

Q12: Convert the decimal number 386 to hex.
Answer:
Answer: 182

Q13: Convert the hex number 386 to decimal.
Answer:
Answer: 902

Q14: Convert the hex number B to decimal.
Answer:
Answer: 11

Q15: If reading the byte 0x21 as a number, what decimal number would it mean?
Answer:
Answer: 33

Q16: Continues in Part-2
12 changes: 7 additions & 5 deletions number-systems/Part-2.md
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Expand Up @@ -7,16 +7,18 @@ The goal of these exercises is for you to gain an intuition for binary numbers.
The answers to these questions will require a bit of explanation, not just a simple answer.

Q16: How can you test if a binary number is a power of two (e.g. 1, 2, 4, 8, 16, ...)?
Answer:
Answer: If there is just one 1 in a binary number, then it is a power of 2. This is because each bit represents a power of 2, so if there is just one 1 bit in a binary number, the value represents a power of 2.

Q17: If reading the byte 0x21 as an ASCII character, what character would it mean?
Answer:
Answer: !

Q18: 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: It represents 33, which is in the range of 0–255 from dark to light. This value represents a very dark grey.

Q19: If reading the bytes 0xAA00FF as a sequence of three one-byte decimal numbers, what decimal numbers would they be?
Answer:
Answer: three one-byte =>
AA | 00 | FF ==> AA : 10 * 16 + 10 * 1 = 170 | 00 : 0 * 16 + 0 * 1 = 0 | FF : 15 * 16 + 15 * 1 = 255
so it reperesnt 170, 0, 255

Q20: 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: AA => 170 Red, 00 => 0 green , FF : 255 is blue

@LonMcGregor LonMcGregor Aug 1, 2026

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These are correct for the individual components, if you combined them together, what colour would that be?

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