fix: Correct Binary Addition error (1+1=10) and clarify Sum/Carry

[kush124k]

Description

This PR addresses a critical content error in the Binary Addition chapter (_docs/binary-algebra/addition.md). The original code block incorrectly stated 1 + 1 = 1, which contradicted the explanatory text and is factually incorrect for binary arithmetic.

Changes made:

1. Fixed the Logic Error: Updated the rules list to correctly show 1 + 1 = 10.
2. Added Clarification: Added a "Sum vs Carry" table for easier explanation of Binary Addition.
3. Improved Example: Added a 3-digit addition example (110 + 101) to demonstrate how a carry bit propagates and expands the result from 3 bits to 4 bits hence explaining how to carry.
4. Refined Explanations: Cleaned up the explanatory paragraph to be more concise and accurate.

Related Issue

Fixes #738

Screenshots (Before vs. After)

Before (The Error):

After (My Fix):

Type of Change

• Bug fix (non-breaking change which fixes an issue)
• Documentation update

How Has This Been Tested?

I verified the changes using the VS Code Markdown Preview.

• Confirmed the Table renders with correct alignment.
• Confirmed the Code Blocks are formatted correctly.
• Checked that the new 3-digit example aligns properly.

Checklist

• My code follows the style guidelines of this project
• I have performed a self-review of my own code
• I have commented my code (or documentation), particularly in hard-to-understand areas
• My changes generate no new warnings

Summary by CodeRabbit

• Documentation
  • Corrected binary addition rules to accurately reflect proper carrying behavior.
  • Refined example illustrations with clearer labeling to enhance understanding of binary arithmetic operations.
  • Improved explanatory text for better comprehension of carrying mechanics in binary addition.

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[coderabbitai]

Walkthrough

Documentation corrected to fix an incorrect binary addition rule statement (1 + 1 = 1 → 1 + 1 = 10), simplified and relabeled example blocks with clearer explanations of binary carry operations, and adjusted formatting and headers for consistency.

Changes

Cohort / File(s)	Summary
Binary Addition Documentation Fix docs/binary-algebra/addition.md	Fixed incorrect binary addition rule (1 + 1 = 10 instead of 1); replaced multi-line example with simplified labeled "Example 1" (1+1=10 and 1+0=1); rewrote carrying explanation; added "Example 2" with 4-bit addition (110 + 101 = 1011); updated formatting and section headers

Estimated code review effort

🎯 1 (Trivial) | ⏱️ ~3 minutes

• Verify binary arithmetic correctness (1 + 1 = 10 with carry)
• Confirm example outputs match the corrected rules
• Check formatting consistency with existing documentation style

Pre-merge checks and finishing touches

✅ Passed checks (5 passed)

Check name	Status	Explanation
Description Check	✅ Passed	Check skipped - CodeRabbit’s high-level summary is enabled.
Title check	✅ Passed	The title clearly and concisely summarizes the main changes: fixing the binary addition error (1+1=10) and clarifying sum/carry concepts in the documentation.
Linked Issues check	✅ Passed	The pull request fully addresses all coding requirements from issue #738: corrected the 1+1=10 error, added a Sum vs Carry clarification table, included a multi-bit example demonstrating carry propagation, and refined explanatory text.
Out of Scope Changes check	✅ Passed	All changes in the pull request are directly aligned with fixing the binary addition documentation error and clarifying related concepts as specified in issue #738; no unrelated modifications detected.
Docstring Coverage	✅ Passed	No functions found in the changed files to evaluate docstring coverage. Skipping docstring coverage check.

✨ Finishing touches

🧪 Generate unit tests (beta)

• Create PR with unit tests
• Post copyable unit tests in a comment

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Actionable comments posted: 0

🧹 Nitpick comments (1)

docs/binary-algebra/addition.md (1)

34-38: Consider extracting the truth table for improved rendering and clarity.

The truth table is currently rendered as plain text within a code block. Extracting it as a native markdown table would improve semantic markup and readability, and explicitly labeling the "Carry" column as "Carry Out" would further clarify the bit-wise addition semantics.

Optional refactor:

- | A | B | Carry | Sum |Result |
- | 0 | 0 |   0   |  0  |   0   |
- | 0 | 1 |   0   |  1  |   1   |
- | 1 | 0 |   0   |  1  |   1   |
- | 1 | 1 |   1   |  0  |   10  |

Extract as a native markdown table outside the code block:

| A | B | Carry Out | Sum | Result |
|---|---|-----------|-----|--------|
| 0 | 0 |     0     |  0  |   0    |
| 0 | 1 |     0     |  1  |   1    |
| 1 | 0 |     0     |  1  |   1    |
| 1 | 1 |     1     |  0  |   10   |

Then adjust the code block to contain only the Examples section.

📜 Review details

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Review profile: CHILL

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📥 Commits

Reviewing files that changed from the base of the PR and between 6a01b5d and 3bba857.

📒 Files selected for processing (1)

• docs/binary-algebra/addition.md (1 hunks)

🔇 Additional comments (3)

docs/binary-algebra/addition.md (3)

26-45: Excellent correction and clarification of binary addition rules.

The fix for "1 + 1 = 10" is now correct, and the truth table effectively demonstrates the distinction between carry and sum outputs. Example 1 (11 + 10 = 101) correctly illustrates single-column addition with proper decimal equivalents. All mathematical content is accurate, and the PR objectives are well-addressed.

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48-48: Clear and accurate step-by-step explanation.

The paragraph effectively walks through the carry mechanism in Example 1 and correctly analogizes to decimal addition. This directly supports the learning objective and addresses the PR's goal of clarifying carry behavior.

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50-57: Excellent multi-bit example demonstrating carry propagation.

Example 2 (110 + 101 = 1011) effectively shows how carries propagate across columns and result in bit-width expansion from 3 to 4 bits. This directly addresses the PR objective to demonstrate carry propagation and is well-positioned after the explanatory text.