Bytes per second to Kilobytes per day conversion

How to convert bytes per second to kilobytes per day?

Sure! Let's break down the conversion of 1 Byte per second to Kilobytes per day in both base 10 (decimal) and base 2 (binary) systems.

Base 10 (Decimal)

In the decimal system, 1 kilobyte (KB) is equal to 1,000 bytes.

1. Seconds in a day: There are 24 hours in a day, 60 minutes in an hour, and 60 seconds in a minute. $24 \times 60 \times 60 = 86,400 \text{ seconds in a day}$

2. Bytes per day: If we have 1 Byte per second, in one day, this would be: $1 \text{ Byte/second} \times 86,400 \text{ seconds/day} = 86,400 \text{ Bytes/day}$

3. Kilobytes per day: To convert bytes to kilobytes in the decimal system: $\frac{86,400 \text{ Bytes}}{1,000 \text{ Bytes/KB}} = 86.4 \text{ KB/day}$

Base 2 (Binary)

In the binary system, 1 kibibyte (KiB) is equal to 1,024 bytes.

1. Seconds in a day: Same as above: $86,400 \text{ seconds in a day}$

2. Bytes per day: If we have 1 Byte per second, in one day, this would also be: $1 \text{ Byte/second} \times 86,400 \text{ seconds/day} = 86,400 \text{ Bytes/day}$

3. Kibibytes per day: To convert bytes to kibibytes in the binary system: $\frac{86,400 \text{ Bytes}}{1,024 \text{ Bytes/KiB}} \approx 84.375 \text{ KiB/day}$

Real World Examples

1. 56 Kbps Modem:

   • Speed: 56 kilobits per second (Kbps)
   • Bytes per second: $56,000 \text{ bits/second} / 8 \text{ bits/Byte} = 7,000 \text{ Bytes/second}$
   • Kilobytes per day (Base 10): $7,000 \text{ Bytes/second} \times 86,400 \text{ seconds/day} = 604,800,000 \text{ Bytes/day}$ $\frac{604,800,000}{1,000} = 604,800 \text{ KB/day}$
   • Kibibytes per day (Base 2): $\frac{604,800,000}{1,024} \approx 590,625 \text{ KiB/day}$

2. Ethernet Connection:

   • Speed: 100 megabits per second (Mbps)
   • Bytes per second: $100,000,000 \text{ bits/second} / 8 \text{ bits/Byte} = 12,500,000 \text{ Bytes/second}$
   • Kilobytes per day (Base 10): $12,500,000 \text{ Bytes/second} \times 86,400 \text{ seconds/day} = 1,080,000,000,000 \text{ Bytes/day}$ $\frac{1,080,000,000,000}{1,000} = 1,080,000,000 \text{ KB/day}$
   • Kibibytes per day (Base 2): $\frac{1,080,000,000,000}{1,024} \approx 1,054,687,500 \text{ KiB/day}$

3. Fiber Optic Internet:

   • Speed: 1 gigabit per second (Gbps)
   • Bytes per second: $1,000,000,000 \text{ bits/second} / 8 \text{ bits/Byte} = 125,000,000 \text{ Bytes/second}$
   • Kilobytes per day (Base 10): $125,000,000 \text{ Bytes/second} \times 86,400 \text{ seconds/day} = 10,800,000,000,000 \text{ Bytes/day}$ $\frac{10,800,000,000,000}{1,000} = 10,800,000,000 \text{ KB/day}$
   • Kibibytes per day (Base 2): $\frac{10,800,000,000,000}{1,024} \approx 10,546,875,000 \text{ KiB/day}$

I hope this helps clarify the conversions and provides some perspective with real-world examples!