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London | SDC-Nov-2025 | Ikenna Agulobi | Sprint 1| Number Systems #238

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London | SDC-Nov-2025 | Ikenna Agulobi | Sprint 1| Number Systems #238

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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 is larger than 0111 as the first bit of 1000 is 1 which is greater than the first bit of 0111.

Which is larger: 00100 or 01011?
Answer:
Answer: 01011 is larger 00100 because comparing from the left to the right, the second bit of 01011 (1) is greater than the second bit of 00100 (0).

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: 8bits

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

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

How can you test if a binary number is a power of two (e.g. 1, 2, 4, 8, 16, ...)?
Answer:
Answer: By checking that the binary number has only one bit set to 1 and all other bits are set to Zero. If there are more than one bit set to 1, then the binary is not a power of two.

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: A dark grey colour

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:A purple colour

If reading the bytes 0xAA00FF as a sequence of three one-byte decimal numbers, what decimal numbers would they be?
Answer:
Answer: 0xAA = 170, 0x00 = 0, 0xFF = 255
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