Binary Addition via Decimal Conversion

A straight-to-the-point method: convert each binary number to decimal, add, convert the sum back to binary.

1. Convert Binary to Decimal

Each bit is a power of two (rightmost bit = 2⁰).

Example (6-bit width):

000100₂
= 0·32 + 0·16 + 0·8 + 1·4 + 0·2 + 0·1
= 4₁₀

2. Add the Decimal Values

000100₂ → 4
000011₂ → 3
4 + 3   = 7

3. Convert the Sum Back to Binary

Divide by 2 repeatedly, keep remainders, read them bottom-up.

7 ÷ 2 = 3 r1   ← bit 0
3 ÷ 2 = 1 r1   ← bit 1
1 ÷ 2 = 0 r1   ← bit 2
→ 111₂

Pad with leading zeros to the original bit-width (6 here):

000111₂

4. Full Walk-Through

1. Convert
2. 000100₂ = 4

3. 000011₂ = 3

4. Add

5. 4 + 3 = 7

6. Convert back

7. 7₁₀ = 000111₂

Result

000100₂ + 000011₂ = 000111₂

5. Practice

Convert, add, convert back:

1. 000101₂ + 000010₂
2. 001010₂ + 000101₂
3. 000111₂ + 001001₂

Use the same three-step process and verify your answers.