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...

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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...

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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

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Write a program that converts a given floating point binary number with a 24-bit normalized mantissa...

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Q1.Convert C46C000016 into a 32-bit single-precision IEEE floating-point binary number.

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