From 71d77e6e47a43b6bfe7ef6d43bb0da1393ad5981 Mon Sep 17 00:00:00 2001 From: Ahmad Hmedan Date: Sat, 14 Mar 2026 02:40:08 +0000 Subject: [PATCH 1/2] answer all question --- number-systems/README.md | 65 ++++++++++++++++++++++++++++++++++++++++ 1 file changed, 65 insertions(+) diff --git a/number-systems/README.md b/number-systems/README.md index 77a3bde94..2f62aca88 100644 --- a/number-systems/README.md +++ b/number-systems/README.md @@ -4,6 +4,54 @@ 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: 1110 + +Convert the binary number 101101 to decimal: +Answer: 45 + +Which is larger: 1000 or 0111? +Answer: 1000 + +Which is larger: 00100 or 01011? +Answer: 01011 + +What is 10101 + 01010? +Answer: 100000 + +What is 10001 + 10001? +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: 15 + +How many bits would you need in order to store the numbers between 0 and 255 inclusive? +Answer: 9 bits + +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: 10 bits + +How can you test if a binary number is a power of two (e.g. 1, 2, 4, 8, 16, ...)? +Answer: n & n-1 == 0 + +Convert the decimal number 14 to hex. +Answer: E + +Convert the decimal number 386 to hex. +Answer: 11E + +Convert the hex number 386 to decimal. +Answer: 902 + +Convert the hex number B to decimal.Do not use any tools or programming to solve these problems. Work it out yourself by hand, and fill in the answers. + +Do not convert any binary numbers to decimal when solving a question unless the question explicitly tells you to. + +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: @@ -63,3 +111,20 @@ Answer: If reading the bytes 0xAA00FF as a sequence of three one-byte decimal numbers, what decimal numbers would they be? Answer: + +Answer: 11 + +If reading the byte 0x21 as a number, what decimal number would it mean? +Answer: 33 + +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: + +If reading the bytes 0xAA00FF as an RGB colour, as described in "Approaches for Representing Colors and Images", what colour would it mean? +Answer: purple but I found the answer on google not from the PDF. + +If reading the bytes 0xAA00FF as a sequence of three one-byte decimal numbers, what decimal numbers would they be? +Answer:170 0 255 From 248e3d19f4a9200f00970fc4b766e8cde9f70ca9 Mon Sep 17 00:00:00 2001 From: Ahmad Hmedan Date: Sat, 14 Mar 2026 03:01:29 +0000 Subject: [PATCH 2/2] check the answer --- number-systems/README.md | 73 +++------------------------------------- 1 file changed, 4 insertions(+), 69 deletions(-) diff --git a/number-systems/README.md b/number-systems/README.md index 2f62aca88..fad1773bc 100644 --- a/number-systems/README.md +++ b/number-systems/README.md @@ -26,7 +26,7 @@ What's the largest number you can store with 4 bits, if you want to be able to r Answer: 15 How many bits would you need in order to store the numbers between 0 and 255 inclusive? -Answer: 9 bits +Answer: 8 bits How many bits would you need in order to store the numbers between 0 and 3 inclusive? Answer: 2 bits @@ -35,7 +35,7 @@ How many bits would you need in order to store the numbers between 0 and 1000 in Answer: 10 bits How can you test if a binary number is a power of two (e.g. 1, 2, 4, 8, 16, ...)? -Answer: n & n-1 == 0 +Answer: n > 0 & (n & n-1 ==0) Convert the decimal number 14 to hex. Answer: E @@ -46,72 +46,7 @@ Answer: 11E Convert the hex number 386 to decimal. Answer: 902 -Convert the hex number B to decimal.Do not use any tools or programming to solve these problems. Work it out yourself by hand, and fill in the answers. - -Do not convert any binary numbers to decimal when solving a question unless the question explicitly tells you to. - -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: - -Convert the binary number 101101 to decimal: -Answer: - -Which is larger: 1000 or 0111? -Answer: - -Which is larger: 00100 or 01011? -Answer: - -What is 10101 + 01010? -Answer: - -What is 10001 + 10001? -Answer: - -What's the largest number you can store with 4 bits, if you want to be able to represent the number 0? -Answer: - -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 3 inclusive? -Answer: - -How many bits would you need in order to store the numbers between 0 and 1000 inclusive? -Answer: - -How can you test if a binary number is a power of two (e.g. 1, 2, 4, 8, 16, ...)? -Answer: - -Convert the decimal number 14 to hex. -Answer: - -Convert the decimal number 386 to hex. -Answer: - -Convert the hex number 386 to decimal. -Answer: - Convert the hex number B to decimal. -Answer: - -If reading the byte 0x21 as a number, what decimal number would it mean? -Answer: - -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: - -If reading the bytes 0xAA00FF as an RGB colour, as described in "Approaches for Representing Colors and Images", what colour would it mean? -Answer: - -If reading the bytes 0xAA00FF as a sequence of three one-byte decimal numbers, what decimal numbers would they be? -Answer: - Answer: 11 If reading the byte 0x21 as a number, what decimal number would it mean? @@ -121,10 +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: +Answer: almost 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: purple but I found the answer on google not from the PDF. +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