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Binary to Decimal Converter

BinaryToDecimal Binary (base-2) numbers have only two possible digits: 0 and 1. Most com-
.sb2 puters operate and communicate with binary numbers. Humans, however,
prefer to work with numbers in the decimal (base-10) system. In this sec-
tion, you’ll develop an application that converts binary numbers to their
decimal equivalents. Later, you could use it as a game to test your ability
to perform such conversions.
Let’s first discuss how to convert from binary to decimal. Figure 8-18
shows an example using the binary number 10011011.

× 128 × 64 × 32 × 16 × 8 × 4 × 2 × 1
1 0 0 1 1 0 1 1

128 + 0 + 0 + 16 + 8 + 0 + 2 + 1 = 155

Figure 8-18: Converting a binary number to a decimal number

All we have to do is multiply each binary digit by its corresponding posi-
tional value and add the resulting products. Positional values correspond to
increasing powers of the base from right to left, with the first position hav-
ing a power of 0. Since binary is base 2, the rightmost digit has a positional
0
value of 2 = 1, so you’d multiply the digit by 1. You’d multiply the next digit
2
1
by 2 = 2, the next by 2 = 4, and so on.
Figure 8-19 illustrates the user interface of the binary-to-decimal con-
version application. The program asks the user to input an 8-bit binary
number. It then shows the input number on the Stage with the Bit sprite,
which uses two costumes to represent 0 and 1. The program also computes
the equivalent decimal number, and the Driver sprite, which has a com-
puter costume, displays that value to the user.

Bit sprite

Driver sprite

Figure 8-19: Binary-to-decimal conversion program

198 Chapter 8
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