From fc9b2604fe7b20e4df087edd3344f1eea902a13e Mon Sep 17 00:00:00 2001 From: Ammad Date: Tue, 24 Mar 2026 20:03:18 +0000 Subject: [PATCH 1/2] Answer all the questions --- number-systems/README.md | 40 ++++++++++++++++++++-------------------- 1 file changed, 20 insertions(+), 20 deletions(-) diff --git a/number-systems/README.md b/number-systems/README.md index 77a3bde94..a248c1d48 100644 --- a/number-systems/README.md +++ b/number-systems/README.md @@ -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 because 1000 = 8 whereas 0111 = 7 Which is larger: 00100 or 01011? -Answer: +Answer: 01011 because 01011 = 11 whereas 00100 = 4 What is 10101 + 01010? -Answer: +Answer: 32 because 10101 = 21 and 01010 = 10 What is 10001 + 10001? -Answer: +Answer: 34 because 10001 = 17 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; 0b0000 How many bits would you need in order to store the numbers between 0 and 255 inclusive? -Answer: +Answer: 8 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: 10 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 exactly one 1 bit, or equivalently if n & (n - 1) == 0 (for n > 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: black 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 + (No Green) + (Blue) ≈ A bright 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 From eb79b7a6b6c06f27cd09ec5c8f2fa27c12b54c66 Mon Sep 17 00:00:00 2001 From: Ammad Date: Wed, 25 Mar 2026 16:56:34 +0000 Subject: [PATCH 2/2] Validate against the answers --- number-systems/README.md | 12 ++++++------ 1 file changed, 6 insertions(+), 6 deletions(-) diff --git a/number-systems/README.md b/number-systems/README.md index a248c1d48..2984b21ff 100644 --- a/number-systems/README.md +++ b/number-systems/README.md @@ -17,10 +17,10 @@ Which is larger: 00100 or 01011? Answer: 01011 because 01011 = 11 whereas 00100 = 4 What is 10101 + 01010? -Answer: 32 because 10101 = 21 and 01010 = 10 +Answer: ~~32 because 10101 = 21 and 01010 = 10~~ 11111 (31 in decimal) What is 10001 + 10001? -Answer: 34 because 10001 = 17 +Answer: ~~34 because 10001 = 17~~ 100010 (34 in decimal) What's the largest number you can store with 4 bits, if you want to be able to represent the number 0? Answer: 15; 0b0000 @@ -32,10 +32,10 @@ How many bits would you need in order to store the numbers between 0 and 3 inclu Answer: 2 How many bits would you need in order to store the numbers between 0 and 1000 inclusive? -Answer: 10 +Answer: 10 (Actual answer: 10, but you'd have 23 spare values, so you can actually store between 0 and 1023 with 10 bits.) How can you test if a binary number is a power of two (e.g. 1, 2, 4, 8, 16, ...)? -Answer: A binary number is a power of two if it has exactly one 1 bit, or equivalently if n & (n - 1) == 0 (for n > 0) +Answer: A binary number is a power of two if it has exactly one 1 bit, or equivalently if n & (n - 1) == 0 (for n > 0) (Actual answer: Test that it has exactly one 1.) Convert the decimal number 14 to hex. Answer: E @@ -56,10 +56,10 @@ If reading the byte 0x21 as an ASCII character, what character would it mean? 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: black +Answer: ~~black~~ Dark grey If reading the bytes 0xAA00FF as an RGB colour, as described in "Approaches for Representing Colors and Images", what colour would it mean? -Answer: Red + (No Green) + (Blue) ≈ A bright purple +Answer: Red + (No Green) + (Blue) ≈ A bright purple (Actual answer: Purple) If reading the bytes 0xAA00FF as a sequence of three one-byte decimal numbers, what decimal numbers would they be? Answer: 170, 0, 255