From 8e8aee4560d3be6607d4dd380de6eeb694b8733d Mon Sep 17 00:00:00 2001 From: Priscilla Date: Wed, 16 Jul 2025 13:19:29 +0100 Subject: [PATCH 1/3] number systems exercises1 --- number-systems/README.md | 59 +++++++++++++++++++++++++++++++++------- 1 file changed, 49 insertions(+), 10 deletions(-) diff --git a/number-systems/README.md b/number-systems/README.md index 77a3bde9..0c54999d 100644 --- a/number-systems/README.md +++ b/number-systems/README.md @@ -5,40 +5,79 @@ 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: Divide by 2 and record the remainders, then write the remainders in reverse order +14 / 2 = 7 R 0 +7 / 2 = 3 R 1 +3 / 2 = 1 R 1 +1 / 2 = 0 R 1 + +1110 + Convert the binary number 101101 to decimal: Answer: +2^0 x 1 = 1 +2^1 x 0 = 0 +2^2 x 1 = 4 +2^3 x 1 = 8 +2^4 x 0 = 0 +2^5 x 1 = 32 + +1 + 0 + 4 + 8 + 0 + 32 = 45 + Which is larger: 1000 or 0111? -Answer: +Answer: 1000 is larger than 111 Which is larger: 00100 or 01011? -Answer: +Answer: 01011 is larger because 1011 is larger than 100 What is 10101 + 01010? -Answer: +Answer: + 1 0 1 0 1 ++ 0 1 0 1 0 + +Adding from right to left + +1 + 0 = 1 +0 + 1 = 1 +1 + 0 = 1 +0 + 1 = 1 +1 + 0 = 1 + 11111 What is 10001 + 10001? Answer: + 1 0 0 0 1 ++ 1 0 0 0 1 + +Adding from right to left + +1 + 1 = 10 = 0 carry 1 +0 + 0 + carry 1 = 1 +0 + 0 = 0 +0 + 0 = 0 +1 + 1 = 10 + +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: 1111 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: Convert the decimal number 14 to hex. -Answer: +Answer: E Convert the decimal number 386 to hex. Answer: From 3fe804b469150d6e52bddc2e393dd5f40d8631ae Mon Sep 17 00:00:00 2001 From: Priscilla Date: Wed, 16 Jul 2025 13:21:30 +0100 Subject: [PATCH 2/3] number systems exercises2 --- number-systems/README.md | 40 +++++++++++++++++++++++++++++++++------- 1 file changed, 33 insertions(+), 7 deletions(-) diff --git a/number-systems/README.md b/number-systems/README.md index 0c54999d..92cff03c 100644 --- a/number-systems/README.md +++ b/number-systems/README.md @@ -80,25 +80,51 @@ Convert the decimal number 14 to hex. Answer: E Convert the decimal number 386 to hex. -Answer: +Answer: 386 / 16 = 24 R 2 + 24 / 16 = 1 R 8 + 1 / 16 = 0 R 1 + = 0x182 Convert the hex number 386 to decimal. Answer: +Going from right to left +16^0 x 6 = 1 x 6 = 6 +16^1 x 8 = 16 x 8 = 128 +16^2 x 3 = 256 x 3 = 768 + 768 + 128 + 6 = 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: +16^0 x 1 = 1 x 1 = 1 +16^1 x 2 = 16 x 2 = 32 + 32 + 1 = 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: 0x21 = 33 + The value of 33 out of 255 will be 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: +Answer: There's more blue, less red and no green = Bluish-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 +0xAA +A = 10 +16^0 x 10 = 1 x 10 = 10 +16^1 x 10 = 16 x 10 = 160 + 160 + 10 = 170 + +0x00 += 0 + +0xFF +F = 15 +16^0 x 15 = 1 x 15 = 15 +16^1 x 15 = 16 x 15 = 240 + 240 + 15 = 255 From 977c350312cc155460dd880795f475e526180b64 Mon Sep 17 00:00:00 2001 From: Priscilla Date: Tue, 29 Jul 2025 06:08:38 +0100 Subject: [PATCH 3/3] corrections --- 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 92cff03c..f4802f68 100644 --- a/number-systems/README.md +++ b/number-systems/README.md @@ -74,7 +74,7 @@ How many bits would you need in order to store the numbers between 0 and 1000 in Answer: 10 How can you test if a binary number is a power of two (e.g. 1, 2, 4, 8, 16, ...)? -Answer: +Answer: They all have only 1 bit and other bits are 0 Convert the decimal number 14 to hex. Answer: E