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: 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: 00100
What is 10101 + 01010? Answer: 11111
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: 8 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: power of two will have only 1 bit set to 1 and the rest of the bits set to zero
Convert the decimal number 14 to hex. Answer: E
Convert the decimal number 386 to hex. Answer: 182
Convert the hex number 386 to decimal. Answer: 902
Convert the hex number B to decimal. 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: 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: 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