Computers work with the simplest possible unit of data: a bit (short for binary digit). A bit has value 0 or 1. Groups of 8 bits together make up a byte. Computer memory is discussed in terms of bytes, such as a kilobyte or megabyte. Hexadecimal, or base 16, is used to represent 4 bits as a time, so a byte is represented as 2 hexadecimal digits. Since 24 is 16, each digit in hexadecimal can take on 16 possible values: 0-9 represent zero to nine, and A-F represent ten to fifteen. For example, a byte could be 0xA3, where the 0x prefix is used to indicate hexadecimal (the value of 0xA3 in decimal is 163).
You should memorize the first few powers of 2 (see bottom of this article), and some size prefixes:
| Prefix | Official definition | Informal meaning |
| kilobyte | 103 bytes | 210 bytes |
| megabyte | 106 bytes | 220 bytes |
| gigabyte | 109 bytes | 230 bytes |
| terabyte | 1012 bytes | 240 bytes |
| petabyte | 1015 bytes | 250 bytes |
Depending on who you talk to, a kilobyte is either 103 (1000) bytes, or 210 (1024) bytes. See Jeff Atwood’s blog post about this as a source of discrepancy between hard drives and operating systems [1]. In whatever system used, know that each increase in memory is roughly 1000 times bigger, either 103 or 210.
Common bit manipulations are AND, OR, XOR, NOT, and bit shifts [2]. These operators take in two bits and output a bit. The meanings of these are clear, except XOR, which returns a 1 if exactly one of the input bits was 1 (but not both). OR is represented by |, AND by &, NOT by ~, and XOR by ^. Think about why the following bit properties are true:
| XOR | AND | OR |
| x ^ 0s = x | x & 0s = 0 | x | 0s = x |
| x ^ 1s = ~x | x & 1s = x | x | 1s = 1 |
| x ^ x = 0 | x & x = x | x | x = x |
Some questions use these binary operators in their solution.
Powers of 2 to know:
| Power | Value |
| 0 | 1 |
| 1 | 2 |
| 2 | 4 |
| 3 | 8 |
| 4 | 16 |
| 5 | 32 |
| 6 | 64 |
| 7 | 128 |
| 8 | 256 |
| 9 | 512 |
| 10 | 1024 |