Name: __________ Grade: __________

Title: Converting binary numbers to decimal

OBJECTIVES

In this iLab, you will develop an algorithm to convert binary numbers to decimal numbers, then apply the algorithm to several binary numbers to obtain their decimal equivalent.

II. PROCEDURE

The process of converting a 4-bit binary number to its decimal equivalent is demonstrated in the following steps.

Step 1: For each bit position, write down the base, 2, raised to the power of that bit position. For a 4-bit number, this would be as follows.

2³2²2¹2⁰

Step 2: Below each bit position, convert the power of 2 to its decimal value.

2³ 2² 2¹ 2⁰

8 4 2 1

Step 3: Below the decimal weights, write down the binary number that will be converted. For example, use 1101.

2³ 2² 2¹ 2⁰

8 4 2 1

1 1 0 1

Step 4: In each position, multiply the decimal weight by the binary number (i.e., 8 x 1 = 8, 4 x 1 = 4).

8 4 2 1

X X X X

1 1 0 1

= = = =

8 4 0 1

Step 5: Sum the numbers.

8 + 4 + 0 + 1 = 13

Therefore, the 4-bit number 1101 base 2 (binary) is equivalent to 13 base 10 (decimal).

Problems:

Using the process described above, convert the following 4-bit binary numbers to their decimal equivalents. Record your results.

0011 =

1100 =

Fill in the missing binary or decimal values in the following table.

Extend the process described above and convert the following 8-bit binary numbers to their decimal equivalent. Record your results.

00010011 =

01011001 =

What is the largest binary number that can be generated in 8-bit binary? How did you arrive at this result?

In your own words, describe the process of converting a binary number into its decimal equivalent. This is the algorithm of converting a binary number to its decimal equivalent.

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