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- Question 6 a) The IEEE Standard 754 representation of a floating point number is given as: 01101110110011010100000000000000. Determine the binary value represented by this number. b) Convert each of the following 8-bit two’s complement binary values to decimal. i) 10110111(base 2) ii) 01001101(base 2) iii) 11010111(base 2) iv) 01110111(base 2) c) Discuss the differences between static RAM and dynamic RAMWhat are the differences between 64-bit and 128-bit floating-point representations? "Let's look at one example."6. Show how each of the following floating point values would be stored using IEEE-754single precision data types correctly.a. 34.55b. -201.601 PS: Please do them in a word processor and not hand-written!
- 2. The table of ascii characters is of size 128. This requires 7 bits of data. (When stored in an 8 bit byte the high bit is usually left 0) If we had 3 bits of data to represent characters in a data set, how many characters could our set contain? Question 1 options: 7 3 9 8 41. Write down the mathematical notation for fixed point representationand floating representation and also explain each term. 2. Consider the following machine number in 64 bit and Precisely represent the above machine number in decimal digits. 0 10000000011 1011100100010000000000000000000000000000000000000000I - For the IEEE 754 single-precision floating point, write the hexadecimal representation for the following decimal value: 0.5
- Show Steps Please 19. Assume we are using the simple model for floating-point representation as given in this book (the representation uses a 14-bit format, 5 bits for the exponent with a bias of 15, a normalized mantissa of 8 bits, and a single sign bit for the number): a) Show how the computer would represent the numbers 100.0 and 0.25 using this floating-point format. b) Show how the computer would add the two floating-point numbers in part a by changing one of the numbers so they are both expressed using the same power of 2. c) Show how the computer would represent the sum in part b using the given floating-point representation. What decimal value for the sum is the computer actually storing? Explain.Consider an 8-bit floating point format. In this representation 4 bits are reserved for the mantissa and 3 bits are reserved for the exponent and 1 bit is reserved for the sign of the number. The exponent of the number is stored with a bias = 3. Express the decimal number 4.75 in this 8 bit floating point format. Write down the next bigger representable number in decimal base. B If you would be conducting the following operation using this 8 bit floating point format what would the result of the following calculation be ? 4.75 + 0.05 - 4.75 Express the decimal number 4.75 in this 8 bit floating point format. [10] b) Write down the next bigger representable number in decimal base. [7.5] c) If you would be conducting the following operation using this 8 bit floating point format what would the result of the following calculation be ? 4.75 + 0.05 - 4.751. Assume we are using the simple model for floating-point representation discussed in the class (the representation uses a 14-bit format, 5 bits for the exponent with an Excess-M, a significand of 8 bits, and a single sign bit for the number) Convert -123.075 to the floating-point binary representation. 2. a) What is "Approximation Error" in floating-point representation? b) Why is it happening? c) How can we minimize it? d) How can the character codes be a solution for this?
- If 6.75 is represented in 8 bit binary floating point, what is the mantissa and exponent value?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).What is the smallest 32-bit floating point number f such that 128 + f > 128 ? What is the smallest 32-bit floating point number g such that 1 + g > 1 ? What is the relationship between f and g?