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Structured Programming Fundamentals  «Prev  Next»
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 * 103 + 4 * 102 + 3 * 101 + 7 * 100 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 * 25 + 1 * 24 + 0 * 23 + 1 * 22 + 0 * 21 + 1 * 20 or
1 * 32 + 1 * 16 + 0 * 8 + 1 * 4 + 0 * 2 + 1 * 1
  1. Decimal number system: Base 10 number system.
  2. Binary number system: Base 2 number system.
Here's a table showing the 8-bit binary numbers and their decimal equivalents.

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 28 or 256 numbers. With n bits you can represent 2n 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.