Base Two Counting ... Binary Numbers
"Binary" means two.
Binary counting would be like having humans with one finger and one hand. The finger is either up, or down.
Binary is not a very convenient way of counting for people, but it is great for machines that only operate in two states - OFF, or ON. Such devices are called "binary", or "digital" devices. Computers are binary devices. For the examples below, an ON condition will be represented by a yellow light globe and an OFF condition by a darkened light globe.
a "1" is used to represent ON,
or "HIGH"
a "0" is used to represent OFF, or "LOW"
Rather than use hands and fingers as in the previous screens we will use a string of globes to represent binary counting. For convenience a set of eight globes will be used ...
This pattern of globes represents the binary number 00101011
Binary counting digits follow the same pattern as all counting digits. The value of each "place" is TWICE the value of the place on the right.
The eight places indicated by the globes above are: 128 64 32 16 8 4 2 1 The same pattern of "powers" applies ...
The 'places' (or "Data Lines") from right to left are known as: D7, D6, D5, D4, D3, D2, D1, D0. The digit on the right (D0) is called the "Least Significant Bit" (LSB). The digit on the left (D7) is called the "Most Significant Bit" (MSB).
Consider the following examples ...
1 1 0 0 1 0 0 0
= 128 + 64 + 0 + 0 + 8 + 0 + 0 + 0 = 200 Decimal
0 1 0 0 1 1 1 0
= 0 + 64 + 0 + 0 + 8 + 4 + 2 + 0 = 78 Decimal
Binary Conversion Table
| D7 | D6 | D5 | D4 | D3 | D2 | D1 | D0 |
| 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
Converting Binary to Decimal
| Binary Number | Place Values | Decimal |
| 00001010 | 0 + 0 + 0 + 0 + 8 + 0 + 2 + 0 | 10 |
| 11001101 | 128 + 64 + 0 + 0 + 8 + 4 + 0 + 1 | 205 |
| 10000001 | 128 + 0 + 0 + 0 + 0 + 0 + 0 + 1 | 129 |
| 00000010 | 0 + 0 + 0 + 0 + 0 + 0 + 1 + 0 | 2 |
Try these ...
1. Draw the light globe ON/OFF pattern for binary 10100010 Click here for the answer ...
2. What is the Decimal value of binary 11000001? Click here for the answer ...
Have your teacher check your answers when you have finished.
