Problem 1 Write a program in a language of your choice (preferably Python, or R). Using the following algorithm. procedure add(a, b: positive integers) (the binary expansions of a and b are (an-1an-2...a1a0)2 and (bn-1bn-2...bibo) 2, respectively) C:=0 for j=0 to n-1 d:= [(aj +b; + c)/2] Sj:= aj +b; +c-2d c:= d Sn = C return (S0, S1,..., Sn) (the binary expansion of the sum is (SnSn-1...50)2}
Problem 1 Write a program in a language of your choice (preferably Python, or R). Using the following algorithm. procedure add(a, b: positive integers) (the binary expansions of a and b are (an-1an-2...a1a0)2 and (bn-1bn-2...bibo) 2, respectively) C:=0 for j=0 to n-1 d:= [(aj +b; + c)/2] Sj:= aj +b; +c-2d c:= d Sn = C return (S0, S1,..., Sn) (the binary expansion of the sum is (SnSn-1...50)2}
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 1: Write a Program in a Language of Your Choice
### Description:
Write a program in a language of your choice (preferably Python, or R) using the following algorithm.
### Algorithm:
```plaintext
procedure add(a, b: positive integers)
{the binary expansions of a and b are (aₙ₋₁aₙ₋₂...a₁a₀)₂ and (bₙ₋₁bₙ₋₂...b₁b₀)₂, respectively}
c := 0
for j := 0 to n - 1
d := [(aⱼ + bⱼ + c) / 2]
sⱼ := aⱼ + bⱼ + c - 2d
c := d
sₙ := c
return (s₀, s₁, ..., sₙ) {the binary expansion of the sum is (sₙsₙ₋₁...s₀)₂}
```
### Explanation:
- The procedure `add(a, b)` takes two positive integers, `a` and `b`, as input.
- These integers are represented in binary as sequences of bits.
- The binary expansions of `a` and `b` are given as (aₙ₋₁aₙ₋₂...a₁a₀)₂ and (bₙ₋₁bₙ₋₂...b₁b₀)₂ respectively.
- Initialize a carry value `c` to 0.
- Loop over each bit position `j` from 0 to n-1:
- Calculate the value `d` as the integer division of the sum of the corresponding bits from `a`, `b`, and the carry `c`.
- Assign the result of the bit-wise sum minus double `d` to `sⱼ`.
- Update the carry `c` with the value of `d`.
- After the loop, assign the final carry value `c` to `sₙ`.
- Return the binary expansion of the sum as a sequence of bits (s₀, s₁, ..., sₙ).
### Figure 1: Adding Two Base 2 Numbers
(This may refer to a visual representation like a flowchart or diagram showing the steps taken](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe872339c-719c-4a81-bc7c-37653a99cb41%2Fb3ebeade-7b8e-402d-918d-b96c1132d502%2Fj29kxo6_processed.jpeg&w=3840&q=75)
Transcribed Image Text:## Problem 1: Write a Program in a Language of Your Choice
### Description:
Write a program in a language of your choice (preferably Python, or R) using the following algorithm.
### Algorithm:
```plaintext
procedure add(a, b: positive integers)
{the binary expansions of a and b are (aₙ₋₁aₙ₋₂...a₁a₀)₂ and (bₙ₋₁bₙ₋₂...b₁b₀)₂, respectively}
c := 0
for j := 0 to n - 1
d := [(aⱼ + bⱼ + c) / 2]
sⱼ := aⱼ + bⱼ + c - 2d
c := d
sₙ := c
return (s₀, s₁, ..., sₙ) {the binary expansion of the sum is (sₙsₙ₋₁...s₀)₂}
```
### Explanation:
- The procedure `add(a, b)` takes two positive integers, `a` and `b`, as input.
- These integers are represented in binary as sequences of bits.
- The binary expansions of `a` and `b` are given as (aₙ₋₁aₙ₋₂...a₁a₀)₂ and (bₙ₋₁bₙ₋₂...b₁b₀)₂ respectively.
- Initialize a carry value `c` to 0.
- Loop over each bit position `j` from 0 to n-1:
- Calculate the value `d` as the integer division of the sum of the corresponding bits from `a`, `b`, and the carry `c`.
- Assign the result of the bit-wise sum minus double `d` to `sⱼ`.
- Update the carry `c` with the value of `d`.
- After the loop, assign the final carry value `c` to `sₙ`.
- Return the binary expansion of the sum as a sequence of bits (s₀, s₁, ..., sₙ).
### Figure 1: Adding Two Base 2 Numbers
(This may refer to a visual representation like a flowchart or diagram showing the steps taken
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