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ZA | 25-SDC-July | Luke Manyamazi | Sprint 1 | Number Systems Exercises #89

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ZA | 25-SDC-July | Luke Manyamazi | Sprint 1 | Number Systems Exercises #89

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42 changes: 21 additions & 21 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:
What's the largest number you can store with 4 bits, if you want to be able to represent the number 0?
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

How can you test if a binary number is a power of two (e.g. 1, 2, 4, 8, 16, ...)?
Answer:
Answer: by using the bitwise formula (N & (N - 1)) == 0
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@chinar-amrutkar chinar-amrutkar Jul 20, 2025

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Can you think of a simpler way of doing this?

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@Luke-Manyamazi Luke-Manyamazi Oct 13, 2025

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A number is a power of two if you can keep dividing it by 2 until you reach 1, with no remainders along the way. If at any point there’s a remainder, it’s not a power of two.


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

Convert the decimal number 386 to hex.
Answer:
Answer: 0x182

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: A dark grey shade

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