Number Systems in Mathematics & Computer Architecture
While humans traditionally compute in Decimal (Base 10) due to ten fingers, digital electronic computers operate on binary logic gates (voltage high/low):
The Radix Systems
- Binary (Base 2): Uses symbols
0and1. Standard building block of all CPUs and memory registers. - Octal (Base 8): Uses symbols
0–7. Useful for 3-bit chunking (such as UNIX file permissions: 755, 644). - Hexadecimal (Base 16): Uses
0–9andA–F. Compactly represents 8-bit bytes (0x00 to 0xFF) and HTML/CSS web hex colors (e.g., #2C7A7B).
Frequently Asked Questions (FAQ)
What does each bit represent in an 8-bit byte?
In standard unsigned binary, each bit position represents powers of two from right to left: 2⁰=1, 2¹=2, 2²=4, 2³=8, 2⁴=16, 2⁵=32, 2⁶=64, and 2⁷=128.