Floating-Point Representation. What is the floating-point value for binary 4. a) 11000010100000 using the simple model (14-bit format, 5 bits for the exponent with a bias 15, a normalized significand of 8 bits, and a single sign bit for the number)?
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- A(n) __________ is an integer stored in double the normal number of bit positions.For 10 bits floating point representation using: seeeefffff, what is the bias for denormalized numbers? A. 7 B. 6 C. 4 D. 3 E. 2 What is the range of integers that can be represented using 8 bits 2's complement? A. -127 to 127 B. -128 to 127 C. -127 to 128 D. 0 to 255 E. 0 to 256Given a floating point representation 10110 11101101000 (5-bit exponent and 11-bit significant) 3. if the exponent is in signed magnitude and the significant is in two’s, what are its normalized floating point representation in hexadecimal and its real value in hexadecimal?
- Examples of 8-bit binary representations of the decimal value 30 are shown below. definition a) the opposite of a term; b) Excess-M;?1) Using IEEE 754 representation for single precision floating point, give the 32-bit binary encoding for the numbers below.Show the sign, exponent, and mantissa (significand).a. -2.40625b. 11.2265625 2) Given the following binary number: 1101.0111, what will be its decimal numberequivalent?1)Using IEEE 754 representation for single precision floating point, give the 32-bit binary encoding for the numbers below.Show the sign, exponent, and mantissa (significand).a. -2.40625b. 11.2265625 2) Given the following binary number: 1101.0111, what will be its decimal numberequivalent?
- 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).Calculate (3.41700875 *10-3 + 6.34005625*10-3)* 1.25625* 102 by hand, assuming each of the values are stored in the 16-bit half precision format describedin in the textbook. Assume 1 guard, 1 round bit, and 1 sticky bit, and round to thenearest even. Show all the steps, and write your answer in both the 16-bit floating point format and in decimal.Given a floating point representation 10110 11101101000 (5-bit exponent and 11-bit significant) if the exponent is in two’s and the significant is in one’s, what are its normalized floating point representation in hexadecimal and its real value in hexadecimal?
- Consider a hypothetical 8 bit floating point machine representation with a sign bit, a 3 bit exponent, and a 4 bit mantissa (se1e2e3b1b2b3b4), where the exponent bias is 3 (add 3 to exponent of number to form machine representation). Recall that actual mantissa has 5 bits, since the leading 1 is not stored on the machine. (a) What is the number ?≈2.718 in this 8-bit format? (b) What is the number that (10100111)2 represents in this 8-bit format? (c) What is the upper bound of the relative error when representing a real number in this 8-bit format?6. In IEEE 32-bit representations, the mantissa of the fraction is said to occupy ______ bits. a. 24 b. 23 c. 20 d. 166. Using IEEE 754 representation for single precision floating point, give the 32-bit binary encoding for the numbers below. Show the sign, exponent, and mantissa (significand).b. 11.2265625