From 3a344e7443fb989ff1e821869d276b4e7411481b Mon Sep 17 00:00:00 2001 From: aiah ibrahim Date: Sun, 13 Jul 2025 23:17:15 +0100 Subject: [PATCH 1/2] number system solved --- number-systems/README.md | 48 ++++++++++++++++++++-------------------- 1 file changed, 24 insertions(+), 24 deletions(-) diff --git a/number-systems/README.md b/number-systems/README.md index 77a3bde9..18e9db9a 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 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: +What's the largest number you can store with 4 bits, if you want to be able to represent the number 0? 2^n - 1 +Answer: (2^4) - 1 = 15 -How many bits would you need in order to store the numbers between 0 and 255 inclusive? -Answer: +How many bits would you need in order to store the numbers between 0 and 255 inclusive? 2^n 2^8 = 256 +Answer: 8 bits -How many bits would you need in order to store the numbers between 0 and 3 inclusive? -Answer: +How many bits would you need in order to store the numbers between 0 and 3 inclusive? +Answer: 2 bits How many bits would you need in order to store the numbers between 0 and 1000 inclusive? -Answer: +Answer: 10 bits -How can you test if a binary number is a power of two (e.g. 1, 2, 4, 8, 16, ...)? -Answer: +How can you test if a binary number is a power of two (e.g. 1, 2, 4, 8, 16, ...)? will have exactly one bit set to 1 +Answer: (n > 0) and (n & (n - 1) == 0) Convert the decimal number 14 to hex. -Answer: +Answer: 0xE Convert the decimal number 386 to hex. -Answer: +Answer: 0x182 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 shade of 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: RGB (170,0,255) 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 b9737d838ef805a0c105ce3e5b897dbb49f0f711 Mon Sep 17 00:00:00 2001 From: aiah ibrahim Date: Mon, 14 Jul 2025 21:43:39 +0100 Subject: [PATCH 2/2] number system fixup --- number-systems/README.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/number-systems/README.md b/number-systems/README.md index 18e9db9a..e09ad38f 100644 --- a/number-systems/README.md +++ b/number-systems/README.md @@ -59,7 +59,7 @@ If reading the byte 0x21 as a greyscale colour, as described in "Approaches for Answer: Dark shade of 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: RGB (170,0,255) +Answer: RGB (170,0,255)/ 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