Binary to decimal conversion in scientific calculator

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binary to decimal conversion on a scientific calculator: a comprehensive guide with code example

this tutorial will walk you through the process of converting binary numbers (base-2) to decimal numbers (base-10) using a scientific calculator. we'll cover both manual methods and the calculator's built-in functionalities. we'll also provide a code example in python to illustrate the conversion algorithm.

*understanding binary and decimal systems*

before diving into the how-to, let's quickly recap the basics:

*decimal (base-10):* the number system we use daily. it uses ten digits (0-9). each digit's position represents a power of 10. for example, the number 123 can be broken down as: (1 \* 10^2) + (2 \* 10^1) + (3 \* 10^0) = 100 + 20 + 3 = 123
*binary (base-2):* uses only two digits: 0 and 1. each digit's position represents a power of 2. for example, the binary number 1011 can be broken down as: (1 \* 2^3) + (0 \* 2^2) + (1 \* 2^1) + (1 \* 2^0) = 8 + 0 + 2 + 1 = 11

*methods for binary to decimal conversion*

there are two primary approaches to converting binary to decimal:

1. **manual conversion (positional notation)**: this involves manually calculating the decimal equivalent based on the position of each binary digit.
2. *using a scientific calculator:* most scientific calculators have built-in functionalities to perform base conversions directly.

*1. manual conversion (positional notation - the core concept)*

this method relies on understanding the positional value of each bit in the binary number. here's the step-by-step process:

*step 1: identify the binary digits (bits):* write down the binary number you want to convert.
*step 2: assign positional weights:* starting from the rightmost bit (least significant bit), assign powers of 2 to each bit, increasing from right to left. the rightmost bit has a weight of 2^0, the next bit to the left has a weight of 2^1, then 2^2, and so on.
*step 3: multiply and sum:* ...

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