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London | 25-SDC-July | Mikiyas Gebremichael | Sprint 1 | Number System #67

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London | 25-SDC-July | Mikiyas Gebremichael | Sprint 1 | Number System #67

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number Systrms excercise
Mikiyas-STP Jul 11, 2025
9ea94f4
Could you clarify what you mean by the "last index"?
Mikiyas-STP Aug 6, 2025
62222f0
What would the colour look like? Example answers - orange, black, etc
Mikiyas-STP Aug 6, 2025
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46 changes: 26 additions & 20 deletions number-systems/README.md
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Expand Up @@ -5,61 +5,67 @@ 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:
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 1024 numbers

How can you test if a binary number is a power of two (e.g. 1, 2, 4, 8, 16, ...)?
Answer:
Answer: if the digit at the last index is 1 and all others are 0 it is power of two (except 1 which is 01)
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Could you clarify what you mean by the "last index"?

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Hello @chinar-amrutkar Thankyou for your feedbacks, i tried to include the explanation next to my answer by saying Clarification as Requested by Volunteer. Sorry there was a huge gap on my use of english and hopefully i explained it now.


Clarification As Requested by Volunteer:
when i say last index i was meant the bit at the nth index (eg 8 = 2**3 so the index = 3) must be one and other digits must be 0
i.e a binary number is a power of two if it contains exactly one 1 bit and all other bits are 0.
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: it is 33 from 0(black)-255(white) 0x21 is almost dark gray (close to 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: AA =170, 00 = 0, FF = 255 It is RGB(170,000,255)
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What would the colour look like? Example answers - orange, black, etc

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thankyou, i have figured it out a color with 170 red and full blue is magneta purple.


Clarification As Requested by Volunteer:
this create a magenta-purple color which is a mix of red = 170 and full blue

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