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London | 25-SDC-July | Andrei Filippov | Sprint 1 | Number systems exercises #69

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London | 25-SDC-July | Andrei Filippov | Sprint 1 | Number systems exercises #69

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Expand Up @@ -5,61 +5,77 @@ 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:
```
14 is equals 8 + 4 + 2 + 0
```
Answer: 1110

Convert the binary number 101101 to decimal:
Answer:
```
32 + 0 + 8 + 4 + 0 + 1
```
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:
Answer: 15

How many bits would you need in order to store the numbers between 0 and 255 inclusive?
Answer:
Answer: 7
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@chinar-amrutkar chinar-amrutkar Jul 22, 2025

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Think about what 255 looks like in binary form. How many bits does it have?

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@Droid-An Droid-An Jul 22, 2025 •
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It will be 11111111, so I’ll need 8 bits for this. I completely forgot that the last digit in a binary number represents 2 to the power of 0, not 1.


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: 9
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Think about what 1000 looks like in binary form. How many bits does it have?

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1111101000 has 10 bits, so I need 10 bits. I made the same mistake again - I forgot that the rightmost digit represents 2 to the power of 0.


How can you test if a binary number is a power of two (e.g. 1, 2, 4, 8, 16, ...)?
Answer:
Answer: If the number have only one '1' digit at the start and other digits are 0 - the number is a power of two

Convert the decimal number 14 to hex.
Answer:
Answer: F
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Think again!
Hint - you start counting the alphabets from 10, not 11


Convert the decimal number 386 to hex.
Answer:
```
386 / 16 = 24 reminder 2
24 / 16 = 1 remider 8
```
Answer: 182

Convert the hex number 386 to decimal.
Answer:
```
3 * 16^2 = 3 * 256 = 768
8 * 16^1 = 128
6 * 16^0 = 6
768 + 128 + 6 = 902
```
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: Gray colour with light intensity equals 33
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Why is the gray light?

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I'm not sure I understand the question clearly. Are you asking why the colour is grey, or why it's light instead of dark


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: Shade of purple, since this number represent the mix of red an blue colour, without green

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