You’ve probably heard that computers only understand zeros and ones. So how does a computer go from zeros and ones to colorful graphical interfaces with buttons and web browsers?

This is part one of two episodes that explain this. This episode is focused on a computer’s memory and how that is composed of bits and bytes. It also covers the binary number system by comparing binary with our normal decimal number system. Some of the number system topics are a bit tedious to explain in just words so here are several place values written for you.

In the tables below, the column headings show how the place value for each column is calculated. You’re probably very familiar with the place value system that you learned in grade school but you might not have realized that there is a pattern. This is not just some set of values that you had to memorize.

Each column header shows the base raised to a power. That’s what the superscript shows – raising a number to a power. All this really means is that a number (the base) is multiplied by itself a certain number of times (the power). So for example, 10^{3} means 10 times 10 times 10.

The column that needs the most explanation is the one on the right. This is the ones. And this column will always be the ones in any number system. That’s because any number raised to the power of zero is always one.

### Base 10 place values (Decimal)

10^{7} |
10^{6} |
10^{5} |
10^{4} |
10^{3} |
10^{2} |
10^{1} |
10^{0} |

10,000,000 | 1,000,000 | 100,000 | 10,000 | 1,000 | 100 | 10 | 1 |

### Base 2 place values (Binary)

2^{7} |
2^{6} |
2^{5} |
2^{4} |
2^{3} |
2^{2} |
2^{1} |
2^{0} |

128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |

### Counting in Base 10 and Base 2

Decimal |
Binary |

0 | 0 |

1 | 1 |

2 | 10 |

3 | 11 |

4 | 100 |

5 | 101 |

6 | 110 |

7 | 111 |