Represent, i.e., encode, 262148.140625 into a 32-bit single-precision IEEE-754 FP value. If rounding is needed, use rounding to the nearest FP number. Your answer MUST BE JUST 8 hexadecimal digits. Write each hexadecimal digit in a field by itself.
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- 2. Convert the IEEE 754 single precision binary representation to a decimal number 1001 1001 1011 0000 0000 0000 0000 0000 Note: make sure that in final answer the fraction is in base 10 (at most 3 digits). You don't need to change the power of 2 in a power of 10.In this question, you are provided with an IEEE-754 floating-point number in the form of 8 hexadecimal digits. You are asked to decode this value into its decimal representation. Do NOT use scientific notation. Do NOT round or truncate your answer. Do NOT add any spaces or commas to your answer. If the converted number is positive, do NOT add the plus sign. Your answer will consist of two parts, the integer value and the fraction value. Do not add any insignificant zeros to your answer. For the fraction part, you can start it by a decimal point or by a single 0, followed by a decimal point. Convert, i.e., decode, 0x48804008 from the 32-bit single-precision IEEE-754 FP representation into decimal representation. The integer part of the number is: D The fractional part of the number (including the decimal point) is: b2. Here is a number represented in the IEEE standard single precision format 11010101010101000000000000000000 What is the decimal number represented by this string in the IEEE standard single precision floating point format?
- Find the sum of all the figits in 15/5/2001 then do the following: Convert the sum into 32-bit binary and also Convert the sum into 32-bit, IEEE-754 single precision floating point format.For example, if your date of birth is 15-8-2001, then the sum of its digits would be 17. You shouldconvert it into 32-bit binary and single precision floating point formats.Find the sum of all the digits in15/5/2001 then do the following:Convert the sum into 32-bit binary.And alsoConvert the sum into 32-bit, IEEE-754 single precision floating pois format.For example, if your date of birth is 15-8-2001, then the sum of its digits woukd be 17. You shouldconvert it into 32-bit binary and single precision floating point formats.In a given 32-bit floating-point representation of numbers, if the number of bits of the mantissa is reduced to accommodate an increase in the number of bits of the exponent, this will result in the following: (select the best answer) Increased range of the numbers at the expense of the precision Increased precision of the numbers at the expense of the range Both range and precision increase Both range and precision decrease
- You are asked to design a 16-bit floating point number system to store the lengths of various man-made objects. This system should work in a similar way as the IEEE754 standard. Assume a value stored in the system denotes the length of an object in centimeters, assume also that the maximum length to be stored is 45845.0 centimeters (i.e. length of the biggest man-made oil-tanker, the “Seawise Giant”). Note: This representation has normalized, de-normalized and special cases as you have seen in IEEE754 standard. Answer the questions below: a) Is sign bit needed in this system? Why yes or why not. b) What is the minimum number of bits needed for the exponent? What is the value of the corresponding bias? Show your steps clearly. If you write the values directly without showing the steps, you will not get any point. c) What is the maximum length the system can represent? Please show your steps clearly, otherwise no point will be given.4. The bfloat16 "brain floating point" format is a 16 bit format used in Google's machine learning and AI software. It is a binary floating point format which is very similar to the single precision IEEE-754 format: 1 bit is allocated for the sign, 8 bits for the exponent with a bias of 127, but only 7 bits are allocated for the fraction (the exponent is always chosen so that the first digit of the mantissa is 1, and then only the fraction is stored in memory). (a) What is the approximate decimal precision of a brain floating point? (b) If the bits are stored in the order: sign, exponent, fraction, and 0 corresponds to a positive sign, then calculate the decimal representation of the number stored as 1 00000110 0100010 (c) Given that the largest exponent actually used for numbers is 11111110, what is the largest number that can be expressed as a bfloat 16? (d) Supposing that numbers are truncated (rounded down), what is the maximum absolute rounding error in bfloat16?Create a 4-bit by 3-bit binary multiplier that multiplies a 4-bit number by a 3-bit number. Note: The 4-bit number should be the multiplicand and the 3-bit number should be the multiplier.
- a.Represent the number 1.01011010101 x 2-19 in IEEE Standard 754 single precision floating point binary. b.the IEEE Standard 754 representation of a floating point number is given as: 01101110110011010100000000000000. Determine the binary value represented by this numberSuppose that we use the floating-point format with 12 decimal digits, SEEEMMMMMMMM, to rep- resent a real number, where S is the digit to represent the sign of the mantissa (use 0 for pos- itive and 5 for negative), EEE are the 3 digits to represent the exponent in excess-500 format, MMMMMMMM are the 8 digits to represent the magnitude of the mantissa, and the decimal point of the mantissa is right to the left of MMMMMMMM (i.e., SEEEMMMMMMMM representing the real number +0.MMMMMMMM × 10EEE-500.) When you use this format to represent a real number, in which scenario an overflow will occur and in which scenarios an underflow may occur?Suppose that we use the floating-point format with 12 decimal digits, SEEEMMMMMMMM, to rep- resent a real number, where S is the digit to represent the sign of the mantissa (use 0 for pos- itive and 5 for negative), EEE are the 3 digits to represent the exponent in excess-500 format, MMMMMMMM are the 8 digits to represent the magnitude of the mantissa, and the decimal point of the mantissa is right to the left of MMMMMMMM (i.e., SEEEMMMMMMMM representing the real number +0.MMMMMMMM × 10EEE-500) What are the smallest positive number and the largest positive number that can be represented in this format? Write them in exponential notation.