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Problem 2 Write a program in a language of your choice (preferably Python, or R). Using the following algorithm. procedure multiply(a, b: positive Integers) {the binary expansions of a and bare (an-1an-2...10) and (bn-bn-2...bibo)2, respectively) for j = 0 ton-1 if bj = 1 then c; := a shifted j places else c; := 0 (co, C1..... Cn-1 are the partial products} P:=0 for j:= 0 ton-1 P:=p+Cj return p (p is the value of ab}

Problem 2 Write a program in a language of your choice (preferably Python, or R). Using the following algorithm. procedure multiply(a, b: positive Integers) {the binary expansions of a and bare (an-1an-2...10) and (bn-bn-2...bibo)2, respectively) for j = 0 ton-1 if bj = 1 then c; := a shifted j places else c; := 0 (co, C1..... Cn-1 are the partial products} P:=0 for j:= 0 ton-1 P:=p+Cj return p (p is the value of ab}

Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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## Problem 2: Multiplying Two Base 2 Numbers using an Algorithm in Python or R ### Task Description: Write a program in a language of your choice (preferably Python or R) to multiply two positive integers using the following algorithm. ### Algorithm to Perform Multiplication: ```plaintext procedure multiply(a, b: positive integers) {the binary expansions of a and b are (a_n-1 a_n-2 ... a1 a0)₂ and (b_n-1 b_n-2 ... b1 b0)₂, respectively} for j := 0 to n - 1 if b_j = 1 then c_j := a shifted j places else c_j := 0 {c₀, c₁, ..., c_n-1 are the partial products} p := 0 for j := 0 to n - 1 p := p + c_j return p {p is the value of ab} ``` ### Explanation: 1. **Binary Expansion**: The numbers `a` and `b` are represented in their binary formats. 2. **Iterate through Digits of b**: - For each bit `b_j` of `b`: - If `b_j` is 1, then calculate the partial product `c_j` by shifting `a` left by `j` positions. - If `b_j` is 0, then the partial product `c_j` is 0. 3. **Sum Partial Products**: The final product `p` is obtained by summing all the partial products `c_j`. 4. **Return the Result**: The result `p` is the multiplication of `a` and `b`. ### Diagrammatic Representation: Figure 2: Multiplying two base 2 numbers. This algorithm effectively leverages the properties of binary numbers to perform the multiplication by bitwise shifts and accumulation. By following this algorithm, you can implement a program to perform binary multiplication in any programming language of your choice, such as Python or R.
Transcribed Image Text:## Problem 2: Multiplying Two Base 2 Numbers using an Algorithm in Python or R ### Task Description: Write a program in a language of your choice (preferably Python or R) to multiply two positive integers using the following algorithm. ### Algorithm to Perform Multiplication: ```plaintext procedure multiply(a, b: positive integers) {the binary expansions of a and b are (a_n-1 a_n-2 ... a1 a0)₂ and (b_n-1 b_n-2 ... b1 b0)₂, respectively} for j := 0 to n - 1 if b_j = 1 then c_j := a shifted j places else c_j := 0 {c₀, c₁, ..., c_n-1 are the partial products} p := 0 for j := 0 to n - 1 p := p + c_j return p {p is the value of ab} ``` ### Explanation: 1. **Binary Expansion**: The numbers `a` and `b` are represented in their binary formats. 2. **Iterate through Digits of b**: - For each bit `b_j` of `b`: - If `b_j` is 1, then calculate the partial product `c_j` by shifting `a` left by `j` positions. - If `b_j` is 0, then the partial product `c_j` is 0. 3. **Sum Partial Products**: The final product `p` is obtained by summing all the partial products `c_j`. 4. **Return the Result**: The result `p` is the multiplication of `a` and `b`. ### Diagrammatic Representation: Figure 2: Multiplying two base 2 numbers. This algorithm effectively leverages the properties of binary numbers to perform the multiplication by bitwise shifts and accumulation. By following this algorithm, you can implement a program to perform binary multiplication in any programming language of your choice, such as Python or R.
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