We use digits on a daily basis to quantify and control the things in our lives. We live in a DECIMAL world - base 10 - with digits 0-9.For example: To make license plates that only have 3 DECIMAL (0-9) digits, we could make 1000 unique plates (000-999) which is 10^3.
With computers, we typically put digits together for a wide array of uses, but the computer uses BINARY digits (0-1).
For example, representing colors: How many colors could we represent with 3 BINARY digits? We could represent 8 colors (000-111) which is 2^3.
It is good to develop an intuitive sense of the ranges associated with n bits.
| n | 2^n | Range: unsigned | Range: signed (2's comp.) | Name |
| 1 bit | 2 | 0 .. 1 | 1 bit | |
| 2 bits | 4 | 0 .. 3 | -2 .. 1 | 2 bits |
| 4 bits | 16 | 0 .. 15 | -8 .. 7 | nybble |
| 8 bits | 256 | 0 .. 255 | -128 .. 127 | byte |
| 16 bits | 65,536 (64k) | 0 .. 65,535 | -32,768 .. 32,767 | word |
| 32 bits | 4 billion+ | 0 .. 4,294,967,295 | -2,147,483,648 .. 2,147,483,647 | longword |
| 64 bits | 0 .. 18,446,744,073,709,551,615 | -9,223,372,036,854,775,808 .. 9,223,372,036,854,775,807 | quadword |
How many colors can be represented with 4 bits? 8? 16? 24? 32?
What are the tradeoffs when representing images?
How many bytes of memory can be addressed with 4 bits? 8 ? 16? 20? 30? 32? 64?
Addresses are how long in most machines?
Each address is the address of a what?