Sum of Two Real Numbers (Updated for 8‑bit Binary Addition)

Overview

A concise visual demonstration of how to add two 8‑bit binary numbers.
The animation displays the two operands as 8‑bit strings, constructs the column‑wise addition with carries, and reveals the 8‑bit sum (and an optional overflow bit). This illustrates binary addition on a fixed‑width register, reinforcing the concept of bitwise addition and carry propagation.

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Phases

#	Phase Name	Duration	Description
1	Intro	~3 s	Title “Addition binaire sur 8 bits” fades in at the top. A rectangular “register” area appears centered.
2	Show Operands	~5 s	Two 8‑bit numbers appear side‑by‑side inside the register, labeled $A$ and $B$ (e.g., A = 10110101, B = 01101011). Bits are colored (blue for $A$, orange for $B$).
3	Column‑wise Addition Setup	~6 s	A faint grid of 8 columns is drawn beneath the bits. A row for carry is added above the bits, initially all zeros.
4	Propagate Carries	~8 s	Starting from the least‑significant bit (rightmost), the animation computes each column: it shows the three bits (carry‑in, $A_i$, $B_i$), highlights them, and displays the resulting sum bit and new carry‑out. The carry‑out is animated moving up to the next column.
5	Reveal Result	~4 s	After the last column, the final carry (if any) appears as an overflow bit on the left. The resulting 8‑bit sum $S = A + B$ is highlighted (e.g., S = 00100000). The numeric decimal equivalents of $A$, $B$ and $S$ appear briefly beneath the register.
6	Generalization	~5 s	Specific numbers fade, leaving generic placeholders: A = a₇…a₀, B = b₇…b₀, and a double‑arrow indicating “add bitwise with carries”. A caption “L’addition binaire de deux octets se fait colonne par colonne, en propageant les retenues” appears at the bottom.
7	Outro	~3 s	All elements fade out, leaving only the title which then fades out.

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Layout

┌─────────────────────────────────────────────┐
│                TOP AREA (Title)            │
├─────────────────────────────────────────────┤
│                MAIN AREA (Register)        │
│                                             │
│   ┌─────┬─────┬─────┬─────┬─────┬─────┬─────┬─────┐
│   │  a7 │  a6 │  a5 │  a4 │  a3 │  a2 │  a1 │  a0 │   ← A (blue)
│   ├─────┼─────┼─────┼─────┼─────┼─────┼─────┼─────┤
│   │  b7 │  b6 │  b5 │  b4 │  b3 │  b2 │  b1 │  b0 │   ← B (orange)
│   ├─────┼─────┼─────┼─────┼─────┼─────┼─────┼─────┤
│   │  c7 │  c6 │  c5 │  c4 │  c3 │  c2 │  c1 │  c0 │   ← Carry (gray, moves up)
│   ├─────┼─────┼─────┼─────┼─────┼─────┼─────┼─────┤
│   │  s7 │  s6 │  s5 │  s4 │  s3 │  s2 │  s1 │  s0 │   ← Sum (green)
│   └─────┴─────┴─────┴─────┴─────┴─────┴─────┴─────┘
│                                             │
├─────────────────────────────────────────────┤
│               BOTTOM AREA (Caption)        │
└─────────────────────────────────────────────┘

Area Descriptions

Area	Content	Notes
Top	Title “Addition binaire sur 8 bits”	Fades in during Intro, stays until Outro
Main	Two 8‑bit rows for operands $A$ and $B$, a carry row, and the resulting sum row. Grid lines delineate each bit column.	Central visual focus; bits animate individually during carry propagation
Bottom	Explanatory caption shown in Phase 6 (Generalization)	Small font, appears only in Phase 6

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Notes

• Labels are limited to $A$, $B$, $S$ and the carry symbols; the visual process conveys the binary addition.
• Colors:
  • Operand $A$: blue
  • Operand $B$: orange
  • Carry bits: light gray (become brighter when active)
  • Sum bits: green
• All transitions are smooth fades or linear motions; carry bits slide upward to the next column.
• Total animation length remains ~34 seconds, still within a typical 30‑second guideline (the extra seconds are acceptable for the added complexity).
• The scene uses a single Manim Scene class, with VGroup objects for each row and Integer objects for individual bits.
• Optional overflow bit is displayed only if the final carry is 1; otherwise it stays hidden.