Recall, a floating point number is composed of a sign, mantissa and exponent portion Consider the following floating point number with a 4 bit mantissa and 3 bit (two's complement) exponent S m e 1 0100 110 What is it's corresponding value in decimal? • a) 0.0625 • b)-0.0625 c) 0.3125 . d)-0.3125
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- What are the mantissa and exponent values if 6.75 is represented in 8-bit binary floating-point representation? a) Mantissa is 1011 and exponent is 101 b) Mantissa is 0011 and exponent is 100 c) Mantissa is 1011 and exponent is 100 d) Mantissa is 0011 and exponent is 101The following is a scheme for floating point number representations using 16 bits: s (1) e (6) m (9) Let s, e, and m be the numbers represented in binary in the sign, exponent, and mantissa fields respectively. Then the floating point number represented is (- 1)° (1 + m × 2 °) 2°-31, if the exponent # 111111. 0, otherwise What is the maximum difference between two successive real numbers representable in this system?Floating point numbers are numbers that support decimal points Express the following numbers in hexadecimal IEEE 32-bit floating-point format 320 -62
- Floating 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.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?C program A decimal number between 0 and 32 exclusive can be expressed in binary system as x4x3x2x1x0, where xi ’s are either zero or one. Write a C program that accepts (from the terminal) a decimal number in the above range and prints out the equivalent binary representation.
- The value ofa float type variable is represented using the single-precision 32-bit floating point format of IEEE-754 standard that uses I bit for sign, 8 bits for biased exponent and 23 bits for mantissa. A float type variable X is assigned the decimal value of -1425. The representation of X in hexadecimal notation isThe following Iis a scheme for floating point number representations using 16 bits: (1) C161 m (9) Let s, e, and m be the numbers represenied in binary in the sign, exponent, and mantissa fields respectively. Then the floating point number represented is (-D'+m 2 " if the exponent = 111111 0, otherwise What is the maximum difference between two successive real numbers representable in this systemIn 8-bit binary floating point, what is the mantissa and exponent value of 6.75?
- 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 ValueSuppose we need to write the decimal number 55.3125 in IEEE floating point representation. What is the value of the EXPONENT? 10001000 10000010 1000100 0100010If the mantissa in a 16-bit floating point number is 10 bits long, then this mantissa 1101100000 when converted to base-10 is equal to: a) .8125 b) .8342 c) .0625 d) .84375 e) None among the given choices