You are asked to design a 16-bit floating point number system to store the lengths of various man-made objects. This system should work in a similar way as the IEEE754 standard. Assume a value stored in the system denotes the length of an object in centimeters, assume also that the maximum length to be stored is 45845.0 centimeters (i.e. length of the biggest man-made oil-tanker, the “Seawise Giant”). Note:

VI. Floating point representation Consider a 12-bit variant of the IEEE floating point format as follows: • Sign bit 5-bit exponent with a bias of 15. • 6-bit significand All of the rules for IEEE 754 Standard apply. Fill in the numeric value represented by the following bit patterns. You must write your number in decimal form (e.g. 0.0146485375, -0.0146485375). Bit Pattern 010011101110 111011101011 100101001111 001010111010 Numerical Value

In a certain computer program, two positive integers are added together, resulting in an overflow error. Which of the following best explains why the error occurs? A) The program attempted to perform an operation that is considered an undecidable problem. B) The precision of the result is limited due to the constraints of using a floating-point representation. C) The program can only use a fixed number of bits to represent integers; the computed sum is greater than the maximum representable value. D) The program cannot represent integers; the integers are converted into decimal approximations, leading to rounding errors.

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.

In this question, you are provided with a decimal floating-point number. You are asked to encode this value into its IEEE-754 floating-point representation in the form of 8 hexadecimal digits. If rounding is needed, use rounding to the nearest floating-point number. Do NOT add any spaces or commas to your answer. Represent, i.e., encode, 262148.140625 into a 32-bit single-precision IEEE-754 FP value. If rounding is needed, use rounding to the nearest FP number. Your answer MUST BE JUST 8 hexadecimal digits. Write each hexadecimal digit in a field by itself. B } Ox D R D = = }

Please use C++ In this lab, you need to write a program which, given a seven digit binary input given below, it will check to see if there is a single bit error using the Hamming Code method discussed in lab. For a sample of Hamming Code, the input: 1110101 will reveal that ‘110’ is the location of the error (meaning the sixth slot in the input), so the corrected number would be 1010101, and the actual message transmitted, would be 1011, which is 11 in decimal. You can use this example to test your program to ensure it’s working correctly. Create a program which can, given a 7-bit long input, written in Hamming Code style, do the three following tasks, displaying the results as output.             (1) Determine if there’s an incorrect bit, and if so, where it is.             (2) Display what the CORRECT code should look like (if it needs to be corrected.)             (3) Display the decimal form of the message that was sent, after any needed correction. Remember, when using Hamming…

Convert the decimal number -43.68 to a floating-point number expressed in the 14-bit simple model given in your textbook. Note: in the 14-bit simple model, the left-most bit is the sign, followed by 5 bits for the exponent, followed by 8 bits for the mantissa (There are no implied bits). The exponent is in Excess 15 notation. 101011.1010

Implement the Hamming Code error detection and correction algorithm for a group message to be transmitted over a network. Hamming code algorithm allows the receiver to detect errors that may have been introduced due to many factors such as noise, interference, and many others. -> Assume the following: 1. The sender message length is 2 bytes. The data transmitted to the user is the 2-byte data in addition to the parity bits. 2. The receiver must be able to detect and correct 1-bit error.  Report :In the report you must include an overview of the Hamming code algorithm and you need to show: 1. The detailed calculation of the minimum number of parity bits needed for a message of 2-byte length. 2. Details on how sender generates the parity bits. 3. Details on how thew receiver detects and corrects a 1-bit error.   THANKS., PLEASE GIVE DETAILED DESCRIPTION.

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.

Why must you be careful when comparing floating-point values for equality?