Binary in Computing
Como Computers Think in 1s e 0s
Understand BinaryTodo photo, video, program, e website ultimately exists as patterns of 1s e 0s. Binary isn't apenas outro number sistema—it's o foundation of todos digital technology. Understanding binary reveals como computers work at their mais fundamental level.
Bits e Bytes
O Bit
- Smallest unidade of data
- Single binary digit: 0 ou 1
- "Binary digit" shortened to "bit"
- Can represent two states (yes/no, on/off, true/false)
O Byte
- 8 bits grouped together
- Can represent 2⁸ = 256 diferente values (0-255)
- Padrão unidade for character storage
- Foundation for larger unidades (KB, MB, GB)
Larger Unidades
| Unidade | Size | Values |
|---|---|---|
| Byte | 8 bits | 256 |
| Word (16-bit) | 2 bytes | 65,536 |
| Double word (32-bit) | 4 bytes | ~4.3 billion |
| Quad word (64-bit) | 8 bytes | ~18.4 quintillion |
Como Data Is Represented
Text (Characters)
- ASCII: 7 bits, 128 characters
- Extended ASCII: 8 bits, 256 characters
- Unicode (UTF-8): Variable length, millions of characters
Exemplo: 'A' = 01000001 (65 in decimal)
Numbers
- Integers: Direct binary representation
- Negative numbers: Two's complement
- Decimals: Floating-point (IEEE 754)
Images
- Pixels represented as numbers
- RGB: 3 bytes per pixel (8 bits cada for Red, Green, Blue)
- 1920×1080 image ≈ 6.2 million bytes uncompressed
Audio
- Som waves sampled as numbers
- CD quality: 16-bit samples, 44,100 times per segundo
Binary Arithmetic
Addition
Mesmo as decimal, but carry at 2:
- 0 + 0 = 0
- 0 + 1 = 1
- 1 + 0 = 1
- 1 + 1 = 10 (0, carry 1)
- 1 + 1 + 1 = 11 (1, carry 1)
Exemplo: 1011 + 1101
1011 + 1101 ------ 11000
= 11 + 13 = 24 ✓
Logic Gates
Hardware implements binary operations through logic gates:
Basic Gates
| Gate | Function | Truth |
|---|---|---|
| AND | Ambos inputs must be 1 | 1 AND 1 = 1 |
| OR | At least one input é 1 | 1 OR 0 = 1 |
| NOT | Inverts input | NOT 1 = 0 |
| XOR | Exatamente one input é 1 | 1 XOR 1 = 0 |
| NAND | NOT AND | 1 NAND 1 = 0 |
Complex operations (addition, comparison) são built from combinations of estes simples gates.
Signed Numbers: Two's Complement
Como computers represent negative numbers:
Method
- Invert todos bits
- Add 1
Exemplo: -5 in 8-bit
- 5 = 00000101
- Invert: 11111010
- Add 1: 11111011
- -5 = 11111011
Por que Two's Complement?
- Addition works naturally (no special cases)
- One representation for zero
- Fácil to implement in hardware
Bitwise Operations in Programming
Programming languages provide operators for bit manipulation:
Comuns Operations
- AND (&): Mask certain bits
- OR (|): Set certain bits
- XOR (^): Toggle bits, encryption
- NOT (~): Invert todos bits
- Left shift (<<): Multiply by 2ⁿ
- Right shift (>>): Divide by 2ⁿ
Exemplo: Check if number é mesmo
n & 1 == 0 means n é mesmo
(Último bit determines odd/mesmo)
Binary in Modern Computing
Memory Addresses
- 32-bit: Can address 2³² = 4 GB
- 64-bit: Can address 2⁶⁴ = 16 exabytes
Network Addresses
- IPv4: 32 bits (e.g., 192.168.1.1)
- IPv6: 128 bits
File Sizes
- Todos files são sequences of bytes
- File type determined by content/structure
Encryption
- AES uses 128, 192, ou 256-bit keys
- SHA-256 produces 256-bit hashes
Conclusão
Binary é o language of todos digital systems because electronic components naturally têm two states. Todo piece of digital data—text, images, audio, video, programs—é ultimately represented as patterns of bits. Understanding binary illuminates como computers work: from o logic gates performing operations to o bytes storing characters to o bits flying across networks. While we rarely interact com binary directly, it underlies everything in o digital mundo.