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: 32+8+4+1 = 45 AND It can be -19 as well, 010011 => 16+2+1 = 19 but negative
Which is larger: 1000 or 0111? Answer: If consider as UNsigned binary: 1000 as 8 > 7 OR If consider as Signed binary: 0111 as 7 > -8 0111 + 1 = 1000 => -8
Which is larger: 00100 or 01011? Answer: 01011
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: 2^n - 1 => 2^10 - 1 = 1023 => 10 bits
How can you test if a binary number is a power of two (e.g. 1, 2, 4, 8, 16, ...)?
Answer: I can check if the binary number include ONLY one "1", its a power of two, since each bit represent a power two. **But I dont know what you mean by the word "test" here**
Convert the decimal number 14 to hex. Answer: E
Convert the decimal number 386 to hex. Answer: 386/16 = 24 and 2 remainder 24/16 = 1 and 8 remainder 1/16 = 0 and 1 remainder So 182
Convert the hex number 386 to decimal. Answer: 16^2 * 3 = 768 16^1 * 8 = 128 16^0 * 6 = 6 So 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: According to ASCII table it`s !
If reading the byte 0x21 as a greyscale colour, as described in "Approaches for Representing Colors and Images", what colour would it mean?
Answer: Since greyscale colour range can be from 0 (black) to 255 (white), and 0x21 = 0d33, So it means Very Dark Gray close to 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: Since we got AA = 170 Red, 00 = no Green, FF = 255 Blue, it representing Dark Blue close to Purple
If reading the bytes 0xAA00FF as a sequence of three one-byte decimal numbers, what decimal numbers would they be?
Answer: 1st byte AA = 170
2nd byte 00 = 0
3rd byte FF = 255