Bytes per second to Kibibits per day conversion

How to convert bytes per second to kibibits per day?

Sure! Let's go through the conversion of 1 Byte per second (Bps) to Kibibits per day, paying attention to both base 10 (metric) and base 2 (binary) systems.

Base 2 (Binary) System:

1. Understanding units:

   • 1 Byte (B) = 8 bits = 1 Bps × 8 bits
   • 1 Kibibit (Kibit) = $2^{10}$ bits = 1024 bits

2. Convert Bytes per second to bits per second:

   • 1 Bps × 8 bits/B = 8 bits per second (bps)

3. Convert bits per second to Kibibits per second:

   • 8 bps ÷ 1024 bit/Kibit = $\frac{8}{1024}$ Kibibits/second = $\frac{1}{128}$ Kibibits/second

4. Convert Kibibits/second to Kibibits/day:

   • $\frac{1}{128}$ Kibibits/second × 60 seconds/minute × 60 minutes/hour × 24 hours/day
   • $\frac{1}{128}$ Kibibits/second × 86400 seconds/day
   • $\frac{86400}{128}$ Kibibits/day = 675 Kibibits/day

So, in the binary system, 1 Byte per second equals 675 Kibibits per day.

Base 10 (Metric) System:

1. Understanding units:

   • 1 Byte (B) = 8 bits = 1 Bps × 8 bits
   • 1 Kilobit (Kbit) = $10^3$ bits = 1000 bits

2. Convert Bytes per second to bits per second:

   • 1 Bps × 8 bits/B = 8 bits per second (bps)

3. Convert bits per second to Kilobits per second:

   • 8 bps ÷ 1000 bit/Kbit = $\frac{8}{1000}$ Kilobits/second = 0.008 Kilobits/second

4. Convert Kilobits/second to Kilobits/day:

   • 0.008 Kilobits/second × 60 seconds/minute × 60 minutes/hour × 24 hours/day
   • 0.008 Kilobits/second × 86400 seconds/day
   • 691.2 Kilobits/day

So, in the metric system, 1 Byte per second equals 691.2 Kilobits per day.

Real-World Examples:

• Modem Speed (Old Dial-Up): Typically around 56 Kbps (Kilobits per second). In Kibibits/day: $56,000 ÷ 1024 \approx 54.688$ Kibibits/s and then $54.688 \times 86400 ≈ 4,731,763$ Kibibits/day.
• Typical Home Internet (2023): 100 Mbps (Megabits per second). In Kibibits/day: $100,000,000 ÷ 1024 = 97,656.25$ Kibibits/s and then $97,656.25 \times 86400 ≈ 8,440,320,000$ Kibibits/day (approximately).
• High-Speed Data Transfer (Data Center): 10 Gbps (Gigabits per second). In Kibibits/day: $10,000,000,000 ÷ 1024 = 9,765,625$ Kibibits/s and then $9,765,625 \times 86400 ≈ 842,445,000,000$ Kibibits/day (approximately).

These examples provide a range of data transfer rates from everyday internet usage to high-speed data transfer scenarios.