Converting 101 from Base 2 to Base 10
To convert the number 101 from base 2 to base 10, we use the formula for base conversion:
\[ \text{Decimal value} = d_n \times 2^n + d_{n-1} \times 2^{n-1} + \ldots + d_1 \times 2^1 + d_0 \times 2^0 \]
Step-by-Step Conversion
For 101 in base 2:
- d₂ = 1
- d₁ = 0
- d₀ = 1
Decimal value = 1 × 2² + 0 × 2¹ + 1 × 2⁰
= 4 + 0 + 1
= 5
Final Result
So, 101 in base 2 is equal to 5 in base 10.
Converting 11 from Base 2 to Base 10
To convert the number 11 from base 2 to base 10, we use the formula for base conversion:
\[ \text{Decimal value} = d_n \times 2^n + d_{n-1} \times 2^{n-1} + \ldots + d_1 \times 2^1 + d_0 \times 2^0 \]
Step-by-Step Conversion
For 11 in base 2:
- d₁ = 1
- d₀ = 1
Decimal value = 1 × 2¹ + 1 × 2⁰
= 2 + 1
= 3
Final Result
So, 11 in base 2 is equal to 3 in base 10.
Converting 111000 from Base 2 to Base 10
To convert the number 111000 from base 2 to base 10, we use the formula for base conversion:
\[ \text{Decimal value} = d_n \times 2^n + d_{n-1} \times 2^{n-1} + \ldots + d_1 \times 2^1 + d_0 \times 2^0 \]
Step-by-Step Conversion
For 111000 in base 2:
- d₅ = 1
- d₄ = 1
- d₃ = 1
- d₂ = 0
- d₁ = 0
- d₀ = 0
Decimal value = 1 × 2⁵ + 1 × 2⁴ + 1 × 2³ + 0 × 2² + 0 × 2¹ + 0 × 2⁰
= 32 + 16 + 8 + 0 + 0 + 0
= 56
Final Result
So, 111000 in base 2 is equal to 56 in base 10.