1.1 Compare and contrast notational systems
📘CompTIA ITF+ (FC0-U61)
Binary (Base-2 Number System)
1. What is Binary?
Binary is a number system that computers use to represent and process data. Unlike the decimal system we use every day (which is base-10 with digits 0–9), binary is base-2, which only uses two digits: 0 and 1.
- 0 = off
- 1 = on
Computers use electrical signals to store and process data. A signal can either be on (1) or off (0). This is why binary is the foundation of all computing.
2. Why Computers Use Binary
Computers are made of electronic circuits that can detect two states: voltage present or voltage absent. Representing data in 0s and 1s aligns perfectly with how hardware works.
- Example in IT:
- RAM stores bits as tiny capacitors: charged = 1, discharged = 0.
- Network devices send data in binary as electrical pulses or light pulses.
3. Binary Place Values
Binary numbers are similar to decimal numbers but each position is a power of 2 instead of 10.
Decimal example:
- 345 = (3×100) + (4×10) + (5×1)
Binary example:
- 1011₂ = (1×2³) + (0×2²) + (1×2¹) + (1×2⁰)
- 1011₂ = 8 + 0 + 2 + 1 = 11 in decimal
Binary Place Values Table (for 8-bit example):
| Bit Position | 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
|---|---|---|---|---|---|---|---|---|
| Binary Value | 1 | 0 | 0 | 1 | 0 | 1 | 1 | 0 |
- Here, the binary number 10010110 = 128 + 16 + 4 + 2 = 150 decimal
4. Bits and Bytes
- Bit = 1 binary digit (0 or 1)
- Byte = 8 bits (most common unit for storing data)
Why this matters in IT:
- File sizes: A text file might be 1 KB = 1024 bytes = 8,192 bits
- Memory: 1 GB RAM = ~8 billion bits
5. Converting Between Binary and Decimal
Decimal → Binary (Divide by 2 method):
- Divide the decimal number by 2.
- Write down the remainder (0 or 1).
- Repeat with the quotient until you reach 0.
- Binary number = remainders read from bottom to top.
Example: Convert 13 to binary
- 13 ÷ 2 = 6 remainder 1
- 6 ÷ 2 = 3 remainder 0
- 3 ÷ 2 = 1 remainder 1
- 1 ÷ 2 = 0 remainder 1
- Binary = 1101
Binary → Decimal (Sum of powers of 2):
- 1101₂ = (1×8) + (1×4) + (0×2) + (1×1) = 8 + 4 + 0 + 1 = 13
6. Binary in IT Environments
Binary is everywhere in computing:
| IT Use Case | How Binary Works |
|---|---|
| IP Addresses | IPv4 addresses are 32 bits, like 11000000.10101000.00000001.00000001 for 192.168.1.1 |
| Data Storage | Hard drives and SSDs store everything as 0s and 1s |
| Networking | Ethernet signals are sent as sequences of bits |
| File Permissions (Linux/Unix) | Permissions use 3-bit binary codes (rwx = 111) |
7. Binary Arithmetic (Basic)
Binary can perform addition like decimal numbers:
| Binary Addition |
|---|
| 0 + 0 = 0 |
| 0 + 1 = 1 |
| 1 + 0 = 1 |
| 1 + 1 = 10 (write 0, carry 1) |
Example: 1011 + 1101
1011
+ 1101
-------
11000
- Computers use this for calculations, logical operations, and processing instructions.
8. Key Terms for the Exam
- Bit = single binary digit (0 or 1)
- Byte = 8 bits
- Nibble = 4 bits
- Base-2 = binary number system
- Binary place value = powers of 2
Summary
- Binary = foundation of all computing
- Only 0 and 1 are used
- Computers use it to store, process, and transmit data
- Understanding binary helps with networking, storage, permissions, and programming basics
