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London | Nadika Zavodovska | Module-Tools | Sprint 1 | Number Systems #22

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London | Nadika Zavodovska | Module-Tools | Sprint 1 | Number Systems #22

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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 (We compare bit by bit from the left. First 1 > 0)

Which is larger: 00100 or 01011?
Answer:
Answer: 01011 (We compare bit by bit from the left. Second 1 > 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 (decimal system), 1111 (binary system)

How many bits would you need in order to store the numbers between 0 and 255 inclusive?
Answer:
Answer: we need 8 bits (11111111(binary) = 255 (decimal))

How many bits would you need in order to store the numbers between 0 and 3 inclusive?
Answer:
Answer: we need 2 bits (11(binary) = 3(decimal))

How many bits would you need in order to store the numbers between 0 and 1000 inclusive?
Answer:
Answer: we need 10 bits (1111101000(binary) = 1000(decimal))
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what would be the largest decimal number you can store with 10 bits?

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@mjpeet, thank you for the interesting question. The largest decimal number that can be stored with 10 bits is 1023. This is because if I convert 1111111111 (binary) to decimal, it equals 1023.


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 only one '1' bit.

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: dark gray

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