Problem 1 . In the C programming language (C99), an int8_t is 8 bits, an int16_t is 16-bits, and an int32_t is 32 bits. Each type is for a specific length of binary bits. Give the range of each type of number in decimal. Show your work.

Problem 2 . At least how many binary bits does it take to represent the decimal number 100,000,000,000? Show your work.

Problem 3 Ordered from Alpha to Omega, the Greek alphabet has 24 characters (Consider the capital characters only). At least how many binary bits should be used to represent the complete Greek alphabet?

Problem 4 Using the number of bits you have obtained from Problem 4, how many more unique characters can you represent in addition to the capital Greek letters?

Problem 5 Study the ones compliment format for signed integers in the textbook section 1.5. Suppose we use half words to store two decimal numbers: 8 and -8. Use the ones compliment, calculate -8+8 and express the result in binary bits using a half word. Also briefly describe your observation on the result.

Problem 6 Restrict us to only five binary bits. Use these five bits to represent unsigned integers. Now calculate 28+6 and 3-12. Express the results using the given five binary bits. Hint: these two calculation will have the problem of overflow. Show your work.