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- 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 Value1) IEEE 754 Floating Point Standard: This standard is used to represent floating-point numbers (real numbers) digitally in computer memory. The standard provides two representations which have different accuracies: double precision and single precision. > Double Precision – 8bytes = 64 bits o Bit 63 (one bit): Sign (0=positive, 1=negative) o Bits 62 to 52 (11 bits): Exponent, biased by 1023 o Bits 51 to 0 (52 bits): Fraction f of the number 1.f Single Precision – 4bytes = 32 bits o Bit 31 (one bit): Sign (0-positive, 1=negative) o Bits 30 to 23 (8 bits): Exponent, biased by 127 o Bits 22 to 0 (23 bits): Fraction f of the number 1.f Procedure to Find the Double-Precision Representation of a Number x: Let the representation be (b63, b62, ..., b, b,, bo) with b63 being the most-significant bit and bo being the least significant bit. Sign Bit: (0, x20 l1, x1 { set new bit as 1 y + y-1 else set new bit as 0 EE 426 Homework 2 Spring 2020/2021 a) Find the double-precision representation of…Problem 3: Compute the mantissa and exponent required to represent 35.436 in base-2 floating point representation.
- Answer the following questions on floating-point representation: a) Convert AD510010 16 to an IEEE single-precision floating-point number b) Convert the following IEEE single-precision floating-point number to a decimal number: 10111111110100000000000000000000I - For the IEEE 754 single-precision floating point, write the hexadecimal representation for the following decimal value: 0.5Floating point calculation: a Show the IEEE 754 representation for the decimal value -0.375 in single precision b. Find the decimal representation for the following single precision floating point number 1011,1111,0111,0000,0000,0000,0000,0000 c. Perform the addition and multiplication of the two floating point numbers in (a) and (b) in binary scientific notation, and represent the sum and product in single precision.
- 1. 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?Taking as a reference the memory representation attached, determine the floating point number stored in it.1) Find the equivalent decimal value of the following floating-point representation using IEEE 754 standard single-precision (32-bit floating-point number with bias = 127) 1 0111 1111 1110 0000 0000 0000 0000 000 (The quiz is expecting a decimal numeric entry. It will automatically suppress leading and trailing zeros. It will display your answer with commas every third digit.) 2) Find an IEEE 754 floating-point representation of -74.2 decimal number. Enter 32 bits without a space. (The quiz is expecting a fill in the blank text string in the entry box and grades on an exact match with the expected result. The answer should be formatted as a 32-bit IEEE 745 binary number representation)
- D&cmid%3D11597 Update E This course EHide blocks Select the correct answer that corresponds to the decimal value of the following number in fixed-point representation: 111.0001 Select one: O a. 7.00625 O b. 7.25 O c. 6.0625 O d. 7.625 O e. 7.0625 A SIGNAL y is declared of STD LOGIC_VECTOR type of 4 bits, if you want to assign 1001 to y, then what is the write assignment statement? Select one: O a. y <= "1001" b. y = "1001" Oc.y= "1001" Od. None of the optionsFind the following floating point representations:¹ (a) f(1/6) (b) fl(11.3) (c) fl(0.4)2. Constrained by the size of the register in your old personal computer at home, youdecide to build a computer with a larger floating point register called R. Five octitscan be represented in R. You decide on the following format for the representation offloating point numbers:R: sign characteristic mantissaYou have available a 1 octit characteristic and a 3 octit mantissa.(b) Write the following decimal numbers as they would be represented in R: (i) 9.25 (ii) -3.5