Question #1:Do problem 2.86 in the text (representation of numbers)Question #2:Do problem 2.87 in the text (more representation)Question #3:2.88 (p. 129) Determine whether or not each expression will always evaluate to 1 (true). If not, briefly explain why (writing 1-2 sentences at most keep it short!). Keep in mind that very large/small values may cause overflow, truncation/rounding, or evaluate to infinity or NaN.Question #4:2.88 Work out long hand the steps to represent 3.1415 as a floating point number using the 8-bit representation on page 106. First, write 3.1415 as a binary number (i.e. it will start with 11 since that represents 3). Then adjust it normalized form (a single 1 before the binary point) and then cast it into the 8-bit representation. You obviously cant represent all of Pi.The following link may help you solve this problem.https://www.youtube.com/watch?feature=player embedded&v=OCYZTg3jahUI HAVE UPLOADED THE TEXT Document Preview: 128 Chapter 2 Representing and Manipulating Information /* Get the sign bits */unsigned sx = ux >> 31; unsigned sy = uy >> 31; /* Give an expression using only ux, uy, sx, and sy */return ; }2.84 ! Given a floating-point format with a k-bit exponent and an n-bit fraction, write formulas for the exponent E, significand M, the fraction f , and the value V for the quantities that follow. In addition, describe the bit representation. A. The number 7.0 B. The largest odd integer that can be represented exactly C. The reciprocal of the smallest positive normalized value 2.85 ! Intel-compatible processors also support an extended precision floating-point format with an 80-bit word divided into a sign bit, k = 15 exponent bits, a single integer bit, and n = 63 fraction bits. The integer bit is an explicit copy of the implied bit in the IEEE floating-point representation. That is, it equals 1 for normalized values and 0 for denormalized values. Fill in the following table giving the approximate values of some interesting numbers in this format: Extended precision Description Value Decimal Smallest positive denormalized Smallest positive normalized Largest normalized 2.86 ! Consider a 16-bit floating-point representation based on the IEEE floating-point format, with one sign bit, seven exponent bits (k = 7), and eight fraction bits (n = 8). The exponent bias is 27-1 1= 63. Fill in the table that follows for each of the numbers given, with the following instructions for each column: Hex: The four hexadecimal digits describing the encoded form. M: The value of the significand. This should be a number of the form x or xy , where x is an integer, and y is an integral power of 2. Examples include: 0, 67 64 , and 1 256 . E: The integer value of the exponent. V : The numeric value represented. Use the notation x or x ? 2z, where x and z are integers.Homework Problems 129 As an example, to represent the number 78 , we would have s = 0, M = 74 , and E = -1. Our number would Attachments: problems-chap.pdf; Question #1:Do problem 2.86 in the text (representation of numbers)Question #2:Do problem 2.87 in the text (more representation)Question #3:2.88 (p. 129) Determine whether or not each expression will always evaluate to 1 (true). If not, briefly explain why (writing 1-2 sentences at most keep it short!). Keep in mind that very large/small values may cause overflow, truncation/rounding, or evaluate to infinity or NaN.Question #4:2.88 Work out long hand the steps to represent 3.1415 as a floating point number using the 8-bit representation on page 106. First, write 3.1415 as a binary number (i.e. it will start with 11 since that represents 3). Then adjust it normalized form (a single 1 before the binary point) and then cast it into the 8-bit representation. You obviously cant represent all of Pi.The following link may help you solve this problem.https://www.youtube.com/watch?feature=player embedded&v=OCYZTg3jahUI HAVE UPLOADED THE TEXT Document Preview: 128 Chapter 2 Representing and Manipulating Information /* Get the sign bits */unsigned sx = ux >> 31; unsigned sy = uy >> 31; /* Give an expression using only ux, uy, sx, and sy */return ; }2.84 ! Given a floating-point format with a k-bit exponent and an n-bit fraction, write formulas for the exponent E, significand M, the fraction f , and the value V for the quantities that follow. In addition, describe the bit representation. A. The number 7.0 B. The largest odd integer that can be represented exactly C. The reciprocal of the smallest positive normalized value 2.85 ! Intel-compatible processors also support an extended precision floating-point format with an 80-bit word divided into a sign bit, k = 15 exponent bits, a single integer bit, and n = 63 fraction bits. The integer bit is an explicit copy of the implied bit in the IEEE floating-point representation. That is, it equals 1 for normalized values and 0 for denormalized values. Fill in the following table giving the approximate values of some interesting numbers in this format: Extended precision Description Value Decimal Smallest positive denormalized Smallest positive normalized Largest normalized 2.86 ! Consider a 16-bit floating-point representation based on the IEEE floating-point format, with one sign bit, seven exponent bits (k = 7), and eight fraction bits (n = 8). The exponent bias is 27-1 1= 63. Fill in the table that follows for each of the numbers given, with the following instructions for each column: Hex: The four hexadecimal digits describing the encoded form. M: The value of the significand. This should be a number of the form x or xy , where x is an integer, and y is an integral power of 2. Examples include: 0, 67 64 , and 1 256 . E: The integer value of the exponent. V : The numeric value represented. Use the notation x or x ? 2z, where x and z are integers.Homework Problems 129 As an example, to represent the number 78 , we would have s = 0, M = 74 , and E = -1. Our number would Attachments: problems-chap.pdf
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