From 66a9c4111361cee4bf4014843017ebe26c671f37 Mon Sep 17 00:00:00 2001 From: Konvaly Date: Wed, 22 Jul 2026 22:54:32 +0100 Subject: [PATCH 1/3] feat: add answers to Q1-Q15 number systems conversions --- number-systems/Part-1.md | 32 ++++++++++++++++---------------- 1 file changed, 16 insertions(+), 16 deletions(-) diff --git a/number-systems/Part-1.md b/number-systems/Part-1.md index d8f9c290e..b357e0f7f 100644 --- a/number-systems/Part-1.md +++ b/number-systems/Part-1.md @@ -7,48 +7,48 @@ The goal of these exercises is for you to gain an intuition for binary numbers. The answers to these questions should be a number, either in binary, hex, or decimal. Q1: Convert the decimal number 14 to binary. -Answer: +Answer: 1110 Q2: Convert the binary number 101101 to decimal: -Answer: +Answer: 45 Q3: Which is larger: 1000 or 0111? -Answer: +Answer: 1000 Q4: Which is larger: 00100 or 01011? -Answer: +Answer: 01011 Q5: What is 10101 + 01010? -Answer: +Answer: 11111 Q6: What is 10001 + 10001? -Answer: +Answer: 11100 Q7: 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 Q8: How many bits would you need in order to store the numbers between 0 and 255 inclusive? -Answer: +Answer: 8 Q9: How many bits would you need in order to store the numbers between 0 and 3 inclusive? -Answer: +Answer: 2 Q10: How many bits would you need in order to store the numbers between 0 and 1000 inclusive? -Answer: +Answer: 10 Q11: Convert the decimal number 14 to hex. -Answer: - +Answer: E + Q12: Convert the decimal number 386 to hex. -Answer: +Answer: 182 Q13: Convert the hex number 386 to decimal. -Answer: +Answer: 902 Q14: Convert the hex number B to decimal. -Answer: +Answer: 11 Q15: If reading the byte 0x21 as a number, what decimal number would it mean? -Answer: +Answer: 33 Q16: Continues in Part-2 From 407d7a176ad4dbd8c08c01a543f34a69a4abcd97 Mon Sep 17 00:00:00 2001 From: Konvaly Date: Wed, 22 Jul 2026 23:33:19 +0100 Subject: [PATCH 2/3] feat: add answers to Q16-Q20 powers of two and multi-byte interpretation --- number-systems/Part-2.md | 16 +++++++++++----- 1 file changed, 11 insertions(+), 5 deletions(-) diff --git a/number-systems/Part-2.md b/number-systems/Part-2.md index 68b0933d9..862d643ff 100644 --- a/number-systems/Part-2.md +++ b/number-systems/Part-2.md @@ -7,16 +7,22 @@ The goal of these exercises is for you to gain an intuition for binary numbers. The answers to these questions will require a bit of explanation, not just a simple answer. Q16: How can you test if a binary number is a power of two (e.g. 1, 2, 4, 8, 16, ...)? -Answer: +Answer: A power of two in binary has only one 1 bit, followed by zero or more 0 bits: 2² = 4 = 100₂, 2⁴ = 16 = 10000₂ Q17: If reading the byte 0x21 as an ASCII character, what character would it mean? -Answer: +Answer: (2 × 16) + (1 × 1) = 32 + 1 = 33₁₀ ASCII value 33 = character '!' Q18: 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: 0x21 = 33₁₀ If we consider greyscale range: 0 (black) to 255 (white), 33 is very close to 0, so it's a very dark grey Q19: If reading the bytes 0xAA00FF as a sequence of three one-byte decimal numbers, what decimal numbers would they be? -Answer: +Answer: 0xAA = (10 × 16) + (10 × 1) = 160 + 10 = 170₁₀ +0x00 = (0 × 16) + (0 × 1) = 0₁₀ +0xFF = (15 × 16) + (15 × 1) = 240 + 15 = 255₁₀ Q20: 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: Red = 170₁₀ (high, but not maximum) +Green = 0₁₀ (none) +Blue = 255₁₀ (maximum) +Red + Blue = violet/purple +Since Blue is max and Red is substantial, it leans toward Blue-Violet From 654236481fe6db22cb2c77d60d6270e3ead65c9b Mon Sep 17 00:00:00 2001 From: Konvaly Date: Wed, 22 Jul 2026 23:56:55 +0100 Subject: [PATCH 3/3] fix: correct Q6 binary addition answer --- number-systems/Part-1.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/number-systems/Part-1.md b/number-systems/Part-1.md index b357e0f7f..a2d4ef1bc 100644 --- a/number-systems/Part-1.md +++ b/number-systems/Part-1.md @@ -22,7 +22,7 @@ Q5: What is 10101 + 01010? Answer: 11111 Q6: What is 10001 + 10001? -Answer: 11100 +Answer: 100010 Q7: What's the largest number you can store with 4 bits, if you want to be able to represent the number 0? Answer: 15