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Structured Programming Fundamentals
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Lesson 2 | Binary numbers |

Objective | Explain what a binary number is. |

The number system that you are probably most familiar with is the *decimal, or base 10, number system*. When representing a number using
decimal notation, each position in the number corresponds to a power of 10, and each digit of the number can be one of the numerals 0, 1, 2,
3, 4, 5, 6, 7, 8, or 9. For example, the decimal number 6437 represents the sum:

6 * 10^{3} + 4 * 10^{2} + 3 * 10^{1} + 7 * 10^{0} or

6 * 1000 + 4 * 100 + 3 * 10 + 7 * 1

Because computers store data as a sequence of switches that can be either on or off, they use a base 2 number system referred to as the*binary number system*. In this number system, each position in a number corresponds to a power of 2, and each digit can be either the
binary digit 1 or 0. For example, the binary number 110101 represents the following sum, which is equal to 45 in the decimal number
system:

1 * 2^{5} + 1 * 2^{4} + 0 * 2^{3} + 1 * 2^{2} + 0 * 2^{1} + 1 * 2^{0} or

1 * 32 + 1 * 16 + 0 * 8 + 1 * 4 + 0 * 2 + 1 * 1

6 * 10

6 * 1000 + 4 * 100 + 3 * 10 + 7 * 1

Because computers store data as a sequence of switches that can be either on or off, they use a base 2 number system referred to as the

1 * 2

1 * 32 + 1 * 16 + 0 * 8 + 1 * 4 + 0 * 2 + 1 * 1

- Decimal number system: Base 10 number system.
- Binary number system: Base 2 number system.

Binary | Decimal |
---|---|

00000000
00000001 00000010 00000011 00000100 . . . 11111101 11111110 11111111 |
0
1 2 3 4 . . . 253 254 255 |

Note that with 8 bits you can represent 2^{8} or 256 numbers. With n bits you can represent 2^{n} numbers.
Now that you know how to interpret binary numbers, you are ready to proceed to the next lesson, where you will learn how to convert between binary and decimal form.