Conversion From Base Two To Base Ten

 

Converting Base Two to Base Ten

To convert a number from Base Two (Binary) back to Base Ten (Decimal), we multiply each digit by its positional power of 2 (starting from 2⁰ on the far right) and add the results together.

Question 1: Convert 110₂ to Base Ten

Solution:
• (1 × 2²) + (1 × 2¹) + (0 × 2⁰)
• (1 × 4) + (1 × 2) + (0 × 1)
• 4 + 2 + 0 = 6

Answer: 110₂ = 6₁₀

Question 2: Convert 1001₂ to Base Ten

Solution:
• (1 × 2³) + (0 × 2²) + (0 × 2¹) + (1 × 2⁰)
• (1 × 8) + (0 × 4) + (0 × 2) + (1 × 1)
• 8 + 0 + 0 + 1 = 9

Answer: 1001₂ = 9₁₀

Question 3: Convert 1100₂ to Base Ten

Solution:
• (1 × 2³) + (1 × 2²) + (0 × 2¹) + (0 × 2⁰)
• (1 × 8) + (1 × 4) + (0 × 2) + (0 × 1)
• 8 + 4 + 0 + 0 = 12

Answer: 1100₂ = 12₁₀

Question 4: Convert 1111₂ to Base Ten

Solution:
• (1 × 2³) + (1 × 2²) + (1 × 2¹) + (1 × 2⁰)
• (1 × 8) + (1 × 4) + (1 × 2) + (1 × 1)
• 8 + 4 + 2 + 1 = 15

Answer: 1111₂ = 15₁₀

Question 5: Convert 10100₂ to Base Ten

Solution:
• (1 × 2⁴) + (0 × 2³) + (1 × 2²) + (0 × 2¹) + (0 × 2⁰)
• (1 × 16) + (0 × 8) + (1 × 4) + (0 × 2) + (0 × 1)
• 16 + 0 + 4 + 0 + 0 = 20

Answer: 10100₂ = 20₁₀