Question

Convert the following binary numbers to a decimal: 1001, 10101, 1010001, and 1010.1010.

Answer 1

1) 1001

=1 × 2³ + 0 × 2² + 0 × 2¹ + 1 × 2⁰

= 8 + 1 = (9)₁₀

2) 10101

=1 × 2⁴ + 0 × 2³ + 1 × 2² + 0 × 2¹ + 1 × 2⁰

= 16 + 4 + 1 = (21)₁₀

3) 1010001

=1 × 2⁶ + 0 × 2⁵ + 1 × 2⁴ + 0 × 2³ + 0 × 2² + 0 × 2¹ + 1 × 2⁰

= 64 + 16 + 1 = (81)₁₀

4) 1010.1010

= 1 × 2³ + 0 × 2² + 1 × 2¹ + 0 × 2⁰ + 1 × 2⁻¹ + 0 × 2⁻² + 1 × 2⁻³ + 0 × 2⁻⁴

= 8 + 2 + 0.5 + 0.125 = (10.625)₁₀

Step-by-step explanation:

Answer 2

1) 1001

=1 × 2³ + 0 × 2² + 0 × 2¹ + 1 × 2⁰

= 8 + 1 = (9)₁₀

2) 10101

=1 × 2⁴ + 0 × 2³ + 1 × 2² + 0 × 2¹ + 1 × 2⁰

= 16 + 4 + 1 = (21)₁₀

3) 1010001

=1 × 2⁶ + 0 × 2⁵ + 1 × 2⁴ + 0 × 2³ + 0 × 2² + 0 × 2¹ + 1 × 2⁰

= 64 + 16 + 1 = (81)₁₀

4) 1010.1010

= 1 × 2³ + 0 × 2² + 1 × 2¹ + 0 × 2⁰ + 1 × 2⁻¹ + 0 × 2⁻² + 1 × 2⁻³ + 0 × 2⁻⁴

= 8 + 2 + 0.5 + 0.125 = (10.625)₁₀