Consider the half-precision floating-point format, which has five bits for the exponent and ten bits for the significand. Find the decimal (i.e., base 10) number represented by the following bits in the half-precision floating- point format: (a) 0100110001110000. (b) 1000001111111111. (c) 0111110000000000.
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- A number x in 64-bits is presented in double precision floating point form as follows. 1 10000001000 0011100001100000000000000000000000000000000000000000 Find the value of x in decimal representation.X and Y are represented in IEEE single precision floating point notation. Let X = (41D00000)16, Y = (C0000000)16. The result of (x *y) in Decimal isWrite down the mathematical notation for fixed point representationand floating representation and also explain each term. Consider the following machine number in 64 bit and Precisely represent the above machine number in decimal digits. 0 10000000011 1011100100010000000000000000000000000000000000000000
- Give (in decimal) the quantity represented by each of the following IEEE 754 single precision floating point values. (a)10111111100000000000000000000000 (b)00000000000000000000000000000000 (c)01111111111111111111111111111111 (d)11000001110110000000000000000000prt d Give (in decimal) the quantity represented by each of the following IEEE 754 single precision floating point values. (a)10111111100000000000000000000000 (b)00000000000000000000000000000000 (c)01111111111111111111111111111111 (d)11000001110110000000000000000000The IEEE Standard 754 representation of a floating point numberis given as: 01101110110011010100000000000000. Determine thebinary value represented by this number. If a computer’s system clock is 2.4 GHz, calculate the period of thesystem clock. If an 8-bit binary number is used to represent an analog value inthe range from 200 ounces to 700 ounces, what is the resolution ofthe system?
- Convert the decimal number -4.375 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.Consider a 16-bit binary floating point number representation system: + | SE E E E E E m m т m m m m m m The first bit of the exponent is dedicated to its sign. Assume that the mantissa must start with a '1'. Use this system to answer the following question What is the smallest (magnitude) number that can be represented with this system?Consider a new floating point representation, which we will call here the CMPT215Float16 representation. The CMPT215Float16 representation follows the IEEE 754 binary floating point standard, but with smaller-sized fields for the exponent and fraction. In particular, CMPT215Float16 numbers have a 1-bit sign field, followed by a 7-bit exponent field (in biased notation, with a bias of only 63 because of the smaller size of this field), followed by an 8-bit fraction field. Give, in decimal, the quantity represented by the following CMPT215Float16 floating point value: 0100001110100000.
- Find the representation x of the following signed numbers listed below in the base specified on the right. a.- (01100110)2=( x )10 b.- (10110111)2=( x )10 C.- (207)10=( x )2 d.- (-135)10=(× )2 e.- (2D7)16=( x )2 f.- (10110011)2=(x )16 g.- (-5.5)10=( x )2 e.- (11000001010000000000000000001010)2=(x )10 Note: In part e the binary representation on the left corresponds to a real number representation.What is the largest binary number that can be expressed with:(a) 8 bits,(b) 10 bits,(c) 16 bits.In each case, write their decimal and hexadecimal equivalents.What is the decimal value of the following number (which is in single-precision IEEE floating point format?) Show your work and explain what each part of the representation is and how you achieve your final answer. 00111111010000000000000000000000