Question

converting from binary to decimal involves multiplying each digit by the value of its place.

true
false

Explanation:

🆕 New Concept Discovered: Positional Notation
Converting numbers between different bases using place values.

Step 1: Understand positional notation

In any positional numeral system, the value of a number is determined by its digits and their positions. Each position (or place) has a specific weight, which is a power of the base of the system.

• In the decimal system (base 10), the place values are powers of 10: \(10^0 = 1\), \(10^1 = 10\), \(10^2 = 100\), etc.
• In the binary system (base 2), the place values are powers of 2: \(2^0 = 1\), \(2^1 = 2\), \(2^2 = 4\), \(2^3 = 8\), etc.

Step 2: Analyze the conversion process

To convert a binary number (like \(1011_2\)) to a decimal number, we look at each digit (bit) and its position:

$$
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$$

We multiply each binary digit by its corresponding place value and then add the results together:

$$ (1 \times 8) + (0 \times 4) + (1 \times 2) + (1 \times 1) = 8 + 0 + 2 + 1 = 11_{10} $$

Since this process directly involves multiplying each digit by the value of its place, the statement is correct.

Answer:

True