Explain the term masking. How is it useful for data representation? Explain the concept using an example For a floating-point format with a k -bit exponent and an n -bit fraction, give a formula for the smallest positive integer that cannot be represented exactly (because it would require an n + 1 –bit fraction to be exact).

Suppose that we use the floating-point format with 12 decimal digits, SEEEMMMMMMMM, to rep- resent a real number, where S is the digit to represent the sign of the mantissa (use 0 for pos- itive and 5 for negative), EEE are the 3 digits to represent the exponent in excess-500 format, MMMMMMMM are the 8 digits to represent the magnitude of the mantissa, and the decimal point of the mantissa is right to the left of MMMMMMMM (i.e., SEEEMMMMMMMM representing the real number +0.MMMMMMMM × 10EEE-500) What are the smallest positive number and the largest positive number that can be represented in this format? Write them in exponential notation.

Assignment for Computer Architecture The assignment is to create a MIPS program that demonstrates that the associative law fails in addition for floating point numbers (single or double precision). You only need to demonstrate it for single precision. Remember the associative law is a + (b + c) = (a + b) + c. The program’s output should look something like the following where the xxx’s are the numbers you chose. The resulting numbers may be different than mine depending on your choice of a, b, and c. Using a = xxx, b = xxx, and c = xxx a + (b + c) = 0 (a + b) + c = 1   The key is to have two of the number large (one positively and one negatively but equal in magnitude) floating point numbers and the third floating point number very small in comparison. As a side note, the associative law will also fail for multiplication for floating point numbers, but you do not need to demonstrate that. Please don't forget to include comments in this code

An interesting application of a PLA is conversion from the old, obsolete punched cards character codes to ASCII codes. The standard punched cards that were so pop- ular with computers in the past had 12 rows and 80 columns where holes could be punched. Each column corresponded to one character. so each character had a 12-bit code. However, only 96 characters were actually used. Consider an application that reads punched cards and converts the character codes to ASCII. a. Describe a PLA implementation of this application. b. Can this problem be solved with a ROM? Explain.