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London | 26-March-SDC | Ammad Ur Rehman | Sprint 1 | Number Systems #425

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London | 26-March-SDC | Ammad Ur Rehman | Sprint 1 | Number Systems #425

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Answer all the questions
anosidium Mar 24, 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 because 1000 = 8 whereas 0111 = 7

Which is larger: 00100 or 01011?
Answer:
Answer: 01011 because 01011 = 11 whereas 00100 = 4

What is 10101 + 01010?
Answer:
Answer: ~~32 because 10101 = 21 and 01010 = 10~~ 11111 (31 in decimal)

What is 10001 + 10001?
Answer:
Answer: ~~34 because 10001 = 17~~ 100010 (34 in decimal)

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; 0b0000

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

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

How many bits would you need in order to store the numbers between 0 and 1000 inclusive?
Answer:
Answer: 10 (Actual answer: 10, but you'd have 23 spare values, so you can actually store between 0 and 1023 with 10 bits.)

How can you test if a binary number is a power of two (e.g. 1, 2, 4, 8, 16, ...)?
Answer:
Answer: A binary number is a power of two if it has exactly one 1 bit, or equivalently if n & (n - 1) == 0 (for n > 0) (Actual answer: Test that it has exactly one 1.)
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@cjyuan cjyuan Mar 27, 2026

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Do you know how this check, n & (n - 1) == 0 can determine numbers that are power of 2?


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: ~~black~~ Dark grey

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: Red + (No Green) + (Blue) ≈ A bright purple (Actual 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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