What do we do when converting from any base to base ten
ScanSolve AI Answer
Answer
To convert a number from any base to base ten, you multiply each digit by the base raised to the power of its position, starting from zero on the rightmost digit. Then, you sum up all these products.
Step-by-step solution
8 stepsHere's the general formula:
Let a number in base b be represented as dₙdₙ₋₁...d₁d₀.
The equivalent value in base ten is:
(dₙ × bⁿ) + (dₙ₋₁ × bⁿ⁻¹) + ... + (d₁ × b¹) + (d₀ × b⁰)
Identify the base (b) of the number you are converting.
Identify the digits of the number and their positions.
The rightmost digit is at position 0, the next digit to the left is at position 1, and so on.
For each digit, multiply the digit by the base raised to the power of its position.
Sum* all the results from Step 3 to get the base ten equivalent.
For example, to convert the number 1011₂ (base 2) to base ten:
The digits are 1, 0, 1, 1.
The positions are 3, 2, 1, 0 (from left to right).
The base is 2.(1 × 2³) + (0 × 2²) + (1 × 2¹) + (1 × 2⁰)
(1 × 8) + (0 × 4) + (1 × 2) + (1 × 1)
8 + 0 + 2 + 1
11*₁₀
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