Concern the following 16-bit floating point representation: The first bit is the sign of the number...

Concern the following 16-bit floating point representation: The first bit is the sign of the number (0 = +, 1 = -), the next nine bits are the mantissa, the next bit is the sign of the exponent, and the last five bits are the magnitude of the exponent. All numbers are normalized, i.e. the first bit of the mantissa is one, except for zero which is all zeros.

1. What's the smallest difference between two consecutive or adjacent numbers?

2. What's the largest difference between two consecutive or adjacent numbers?(Give both numbers in both binary and decimal representations)

3. Translate .1 decimal into our 16-bit binary floating point representation and translate the result back into decimal. What happened? Why?

4. Give a simple rule for determining when a fraction (i.e. a ratio of two integers) can be represented exactly by a terminating decimal expression(i.e. non-repeating)

5. Give a simple rule for determining when a fraction can be represented exactly by a terminating binary expression (i.e. non-repeating)

6. Do all terminating binary fractions terminate in decimal? Do all terminating decimal fractions terminate in binary

Expert Solution

venereology answered 8 months ago

These questions concern the following 16-bit floating point representation: The first bit is the sign of...

These questions concern the following 16-bit floating point representation: The first bit is the sign of the number (0 = +, 1 = -), the next nine bits are the mantissa, the next bit is the sign of the exponent, and the last five bits are the magnitude of the exponent. All numbers are normalized, i.e. the first bit of the mantissa is one, except for zero which is all zeros. a) What is the largest number? (in both 16-bit...

Consider the following 32-bit floating point representation based on the IEEE floating point standard: There is...

Consider the following 32-bit floating point representation based on the IEEE floating point standard: There is a sign bit in the most significant bit. The next eight bits are the exponent, and the exponent bias is 28-1-1 = 127. The last 23 bits are the fraction bits. The representation encodes number of the form V = (-1)S x M x 2E, where S is the sign, M is the significand, and E is the biased exponent. The rules for the...

c) Using the 32-bit binary representation for floating point numbers, represent the number 1011100110011 as a...

c) Using the 32-bit binary representation for floating point numbers, represent the number 1011100110011 as a 32 bit floating point number. i) A digital camera processes the images images in the real-world and stores them in binary form. Using the principles of digital signal processing, practically explain how this phenomenon occurs.

Convert 0.875 to an IEEE 754 single-precision floating-point number. Show the sign bit, the exponent, and...

Convert 0.875 to an IEEE 754 single-precision floating-point number. Show the sign bit, the exponent, and the fraction. Convert -3.875 to an IEEE 754 double-precision floating-point number. Show the sign bit, the exponent, and the fraction Convert the IEEE 754 single-precision floating-point numbers 42E4800016 and 0080000016 to their corresponding decimal numbers.

Find the 3-bit mantissa floating point representation of the following numbers, both by chopping and rounding,...

Find the 3-bit mantissa floating point representation of the following numbers, both by chopping and rounding, and then calculate the associated respective absolute error and relative error: (a) 11/16 (b) 2.75

Convert the following number into 32bit IEEE 754 floating point representation. 0.000101

Assume that you have a 12-bit floating point number system, similar to the IEEE floating point...

Assume that you have a 12-bit floating point number system, similar to the IEEE floating point standard, with the format shown below and a bias of 7. The value of a floating point number in this system is represented as FP = (-1)^S X 1.F X 2^(E-bias) for the floating point numbers A = 8.75 and B = -5.375. The binary representation of A is given as A = 0101 0000 1100 Show the hexidecimal representation of B.

Convert 1.67e14 to the 32-bit IEEE 754 Floating Point Standard, with the following layout: first bit...

Convert 1.67e14 to the 32-bit IEEE 754 Floating Point Standard, with the following layout: first bit is sign bit, next 8 bits is exponent field, and remaining 23 bits is mantissa field; result is to be in hexadecimal and not to be rounded up. answer choices 5717E27B 57172EB7 5717E2B7 C717E2B7 5771E2B7

The number –11.375 (decimal) represented as a 32-bit floating-point binary number according to the IEEE 754...

The number –11.375 (decimal) represented as a 32-bit floating-point binary number according to the IEEE 754 standard is

Convert the following floating-point number (stored using IEEE floating-point standard 754) to a binary number in...

Convert the following floating-point number (stored using IEEE floating-point standard 754) to a binary number in non-standard form. 0100_0001_1110_0010_1000_0000_0000_0000

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