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- The running time of long integer multiplication is MCQ O(n2.81) O(n3) O(n1.58) O(n2)What is the minimum number of multiplications needed to generate x60 when starting from x? (you may only use terms of x to solve this problem, x * x = x2 is one multiplication, x2 * x2 leaves us at 2 multiplications, …)Scenario: In a biased N-bit binary number system with bias B, positive and negative numbers are represented as their value plus the bias B. For example, for 5-bit numbers with a bias of 15, the number 0 is represented as 01111, 1 as 10000, and so forth. Biased number systems are sometimes used in floating point mathematics. Consider a biased 8-bit binary number system with a bias of 12710 Question: What is the representation and value of the most negative number?
- Hexadecimal multiplication is like decimal multiplication. However, using hexadecimal symbols. For example123x 45 615 + 492 = 5535 Now, perform the following multiplication in hexadecimal and show your work like the decimal example Multiply 0XAF, 0X2C Multiply 0XAFC2, 0X45ACInteger division on most machines is even slower than integer multiplication—requiring 30 or more clock cycles. Dividing by a power of two can also be performed using shift operations. Explain how this helps in performing division. Explain with an example. How is positive and negative infinity represented in the binary number?Find the decimal expansion of (B34F) 16. Fill in the blanks with the appropriate numbers. (B34F) 16 = 10¹ + • 104 + • 10⁰ •10³ + •10² +
- Implement the modular exponentiation (a.k.a. fast exponentiation) function mod_exp (b, n, m) to compute bn (mod m) more efficiently. (Hint: to read n bit-by-bit, use / and % operations repeatedly) a) Test your function for b = 3, n = 231 – 2, m = 231 – 1. b) Report the result and the time (in seconds) it takes to find the result. Q3. [30 pts] Modify your is_prime function to use the mod_exp (b, n, m) instead of the standard power operation (b**n % m). Rename it as is_prime2. Modify the mersenne (p) function to use is_prime2, and call it mersenne2. a) Use the modified function mersenne2 to print all the Mersenne primes Mp for p between 2 and 31 if possible, (with k = 3 in the is_prime function). Compare the results with the ones found in Q1. b) Gradually increase the range of p to find more Mersenne primes (say up to p = 101 if possible). What is the largest Mersenne prime you can achieve here? c) Extend the work in part (b) and find the maximum Mersenne prime you can get from this…Pick two positive integer numbers. Show that if you multiply them, then you will get a negative integer as your result because of overflow. Therefore, you need to demonstrate what happens when overflow happens with two’s complement integer multiplication. You have a 4-bit processor, and the number representation is two’s complement.In MIPS assembly, implement integer division using rounding (rather than truncation). This is accomplished by taking the remainder of the division and dividing it by the original divisor. If the new quotient is higher than or equal to one, multiply it by one.Otherwise, leave the original quotient alone.In MIPS assembly, implement integer division using rounding (rather than truncation). This is accomplished by taking the remainder of the division and dividing it by the original divisor. If the new quotient is higher than or equal to one, multiply it by one.Otherwise, leave the original quotient alone.In MIPS assembly, implement integer division using rounding (rather than truncation). This is accomplished by taking the remainder of the division and dividing it by the original divisor. If the new quotient is higher than or equal to one, multiply it by one.Otherwise, leave the original quotient alone.In MIPS assembly, implement integer division using rounding (rather than truncation).…
- Perform each of the below computation using IEEE-754 single precision representation. [Method: Convert both the given decimal values to IEEE-754 single precision representation. Perform IEEE-754 computation and write the result in hexadecimal. Convert the IEEE-754 single precision hexadecimal result back to decimal value]. Clearly show all the steps. I a. 3.375 + 7.25 = b. 3.375 – 7.25 =ASCII Codes can be helpful to find binary code of different decimal numbers and alphabets etc. You have to consider 65 and its equivalent code of 16 bits will be considered for bit sequence and a divisor for CRC. Follow this process; first 8 bits will be used for data while next 4 bits will be used for divisor (if there are 4 zeroes in your case then replace with 1001), neglect last 4 bits. Also check your answer.Given a bit array A = [ 0 0 1 1 0 1] on which the operations are workable:i) Can you use OR to change any desired bit of A to 1?ii) Can you use AND to change any desired bit of A to 0?iii) Can you use XOR to invert or toggle any desired bit of A?