Technology & Computing: Binary, Aspect Ratios & Transfer Guide
Number base conversions, display aspect ratios, and network bandwidth transfer speeds.
Computing operates on discrete mathematics and binary representation. From calculating exact download times over network connections to verifying screen resolution aspect ratios and password entropy, digital calculations help engineers and creators build better systems.
Where L is password length and R is the size of the character pool (e.g. 94 for printable ASCII). Remember: 1 Byte = 8 bits.
Scenario: Downloading a 5 Gigabyte (GB) file over a 100 Megabit per second (Mbps) internet link.
- File: 5 GB = 5,000 MB
- Connection: 100 Mbps = 12.5 MB/s (100 / 8)
- Convert file to megabits = 5,000 × 8 = 40,000 Megabits
- Divide by bandwidth = 40,000 / 100 = 400 seconds
- Convert to minutes = 400 / 60 = 6 minutes and 40 seconds
- Always verify network capitalization: "b" stands for bits (speed, Mbps) and "B" stands for bytes (storage, MB).
- Standard widescreen displays use 16:9 aspect ratios (e.g. 1920×1080 or 3840×2160); ultrawide uses 21:9.
- A password with 60+ bits of entropy is secure against common automated dictionary attacks; 80+ bits resists brute-force clusters.
- Account for 10% TCP/IP network protocol overhead when planning large server data migrations.
Put the formulas above into practice with these free tools:
Download Time Calculator
How long a file takes to download at a given internet speed.
Number Base Converter
Convert a decimal number to binary, octal, and hexadecimal.
Aspect Ratio Calculator
Simplest aspect ratio and the matching height for a new width.
Password Strength Calculator
Estimate password entropy from its length and character set.
PX to REM Converter
Convert pixels to rem, em, points, and percent for CSS.
Video File Size Calculator
Estimate file size from bitrate and duration.
CIDR / Subnet Host Calculator
Subnet mask and usable host count for a CIDR prefix.
RAID Capacity Calculator
Usable storage and fault tolerance for common RAID levels.
How do you convert decimal numbers to binary?
Repeatedly divide the number by 2, recording the remainders in reverse order (e.g. 13 = 1101 in binary).
What is the difference between 1080p and 4K?
4K UHD (3840×2160) contains four times as many total pixels (8.29 million) as standard 1080p Full HD (2.07 million).
Why does my 1TB hard drive only show 931GB in Windows?
Hard drive manufacturers define 1TB as 10¹² bytes (decimal), while Windows measures in Gibibytes (2⁴⁰ bytes): 1,000,000,000,000 / 1,073,741,824 ≈ 931.32 GiB.