CS101 Assignment 1 Solution 2023
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CS101 Assignment 1 Solution 202 3 Introduction to Computing
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CS101 Assignment No 1 Solution Spring 2023
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Spring 2023 CS101 Solution
Computer science (cs101), virtual university of pakistan.
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Introduction to computing (cs101), assignment no. 01, spring 2023.
As you know computer system stores all types of data as stream of binary digits (0 and 1). This also includes the numbers having fractional values, where placement of radix point is also incorporated along with the binary representation of the value. There are different approaches available in the literature to store the numbers having fractional part. One such method, called Floating-point notation is discussed in your week 03 lessons. The floating point representation needs to incorporate three things:
In the video lessons, 8-bit storage is used to demonstrate the working of floating point notation with the help of examples where 8-bit storage is divided as:
1 bit for Sign.
3 bits for Exponent.
4 bits for Mantissa (the mantissa field needs to be in normalized form as discussed in the video lesson).
For the discussed 8-bit floating point storage:
A. Encode the (negative) decimal fraction -9/2 to binary using the 8-bit floating-point notation. B. Determine the smallest (lowest) negative value which can be incorporated/represented using the 8-bit floating point notation. C. Determine the largest (highest) positive value which can be incorporated/represented using the 8- bit floating point notation.
Step 1: Convert -9/2 to binary:
Convert the absolute value of 9 to binary: 1001.
Convert 1/2 to binary: 0.
Combine the integer and fractional parts: 1001.
Negative the result since the decimal fraction is negative: -1001.
Step 2: Normalize the binary number:
Shift the decimal point to the left until there is only one non- zero digit to the left of the decimal point. We get -1 × 2^3.
Step 3: Determine the sign, exponent, mantissa:
The sign bit is 1 since the number is negative.
The exponent is 3, which is biased by adding 7 (excess-3) to get 10 (binary 1010).
The mantissa is the binary fraction 0011 truncated to 4 bits (since we have 4 bits for the mantissa).
Step 4: Combine the sign, exponent, and mantissa to form the 8-bit floating-point representation:
The sign bit is 1(negative).
The exponent is 1010 (binary 10).
The mantissa is 0011.
Putting it all together, the 8-bit floating-point representation of -9/2 in binary is: 1 1010 0011
Determine the smallest (lowest) negative value which can be incorporated/represented using the 8-bit floating point notation.
- Multiple Choice
Course : Computer science (CS101)
University : virtual university of pakistan.
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