Binary to Decimal and Decimal to Binary Conversion Quiz

Converting Binary to Decimal and Decimal to Binary

Understanding how to convert between binary numbers and decimal numbers is a fundamental skill in computing, where every device and program exchange data using the binary number system.

Binary to Decimal

To convert a binary number to decimal, follow these steps:

1. Write each bit from the rightmost digit to the leftmost digit, with 0s as placeholders if necessary.
2. Create a table with powers of 2, starting with 2^0 = 1.
3. For each bit from right to left, multiply the bit by its corresponding value in the table and add the results to the running total.

For example, let's convert the binary number (11010_2) to decimal:

\begin{tabular}{c|c} (2^4) & 16 \ (2^3) & 8 \ (2^2) & 4 \ (2^1) & 2 \ (2^0) & 1 \ \end{tabular}

(1 \times 16 + 1 \times 8 + 0 \times 4 + 1 \times 2 + 0 \times 1 = 26_{10})

Decimal to Binary

To convert a decimal number to binary, use repeated division by 2 with the following steps:

1. Divide the decimal number by 2, and record the quotient and remainder.
2. If the quotient is zero, finish, and the remainder is the least significant bit (LSB) in the binary number.
3. If the quotient is not zero, divide the quotient by 2 and repeat step 2 until the quotient is zero.
4. Write the remainders from top to bottom, with the last remainder being the most significant bit (MSB).

For example, let's convert 24 to binary:

(24\overbrace{\div 2}^1=12) with remainder 0 (12\overbrace{\div 2}^6=6) with remainder 0 (6\overbrace{\div 2}^3=3) with remainder 1 (3\overbrace{\div 2}^1=1) with remainder 1 (1\overbrace{\div 2}^0=0)

So, (24_d=11110_2)

Patterns and Tips

An odd binary number always ends in 1, and the number of 1s in the binary representation of a decimal number is the same as the decimal number's 1's complement when divided by 2.

For instance, the binary number (1111_2) is odd, and (1111_2=15_d). Dividing 15 by 2, we get a quotient of 7 with a remainder of 1, which is the same number of 1s in (1111_2).

Knowing these patterns can help you to efficiently convert between decimal and binary numbers, and to verify your results.

Practice and Reminders

Regular practice is the best way to become proficient at converting between binary and decimal numbers. It is helpful to draw the bits and powers of 2 on paper or use a calculator to check your work. As always, understanding how the conversion works is more important than memorizing formulas.

Confidence in converting between binary and decimal numbers is a valuable tool for anyone interested in programming, computing, and other fields where binary data is used.