C++ Programming: From Problem Analysis to Program Design
C++ Programming: From Problem Analysis to Program Design
8th Edition
ISBN: 9781337102087
Author: D. S. Malik
Publisher: Cengage Learning
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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
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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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