3. [20 marks] Luffy is a CPSC 121 student and he decided to propose the following...

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3. [20 marks] Luffy is a CPSC 121 student and he decided to propose the following scheme for representing floating point numbers using 12 bits. The leftmost 8 bits will be the signed binary integer x representing the decimal digits that will form the components to both the left and right of the decimal point; the rightmost 4 bits will be a signed binary integer y representing the exponent of 10 by which will be multiplied to produce the final floating point value. Assume that signed integers are encoded using two's-complement. For example, the number -14.35 would have x = -1435 and y -2. a. [5 marks] What is the largest value representable using this scheme? b. [5 marks] scheme? c. [5 marks] scheme? What is the smallest positive (non-zero) value representable using this What's the smallest (i.e., most negative) value representable using this d. [5 marks] Give a number smaller than your answer for item 3a and larger than your answer for item 3c that has 2 digits after the decimal point and it is not representable using this scheme. 3. [20 marks] Luffy is a CPSC 121 student and he decided to propose the following scheme for representing floating point numbers using 12 bits. The leftmost 8 bits will be the signed binary integer x representing the decimal digits that will form the components to both the left and right of the decimal point; the rightmost 4 bits will be a signed binary integer y representing the exponent of 10 by which will be multiplied to produce the final floating point value. Assume that signed integers are encoded using two's-complement. For example, the number -14.35 would have x = -1435 and y -2. a. [5 marks] What is the largest value representable using this scheme? b. [5 marks] scheme? c. [5 marks] scheme? What is the smallest positive (non-zero) value representable using this What's the smallest (i.e., most negative) value representable using this d. [5 marks] Give a number smaller than your answer for item 3a and larger than your answer for item 3c that has 2 digits after the decimal point and it is not representable using this scheme.

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a To find the largest value representable using this scheme we need to consider the maximum value fo... View the full answer