bits per second to Kilobits per day conversion

How to convert bits per second to kilobits per day?

To convert $1 \text{ bits per second (bps)}$ to Kilobits per day, you first need to understand the conversion factors between these units. Kilobits and bits are related by specific factors, and this can be different for base 10 (decimal) and base 2 (binary) systems.

Base 10 Conversion (Decimal System)

In the decimal system (often used in telecommunications), 1 Kilobit = 1000 bits.

1 day = 24 hours = 24 × 60 minutes = 1440 minutes = 1440 × 60 seconds = 86400 seconds.

Steps:

1. Calculate the total number of bits in a day for a given data rate: $1 \text{ bps} \times 86400 \text{ seconds} = 86400 \text{ bits/day}$

2. Convert bits per day to Kilobits per day: $\frac{86400 \text{ bits}}{1000} = 86.4 \text{ Kilobits/day}$

So, in the decimal system: $1 \text{ bits per second} = 86.4 \text{ Kilobits per day}$

Base 2 Conversion (Binary System)

In the binary system, 1 Kibibit = 1024 bits.

Steps:

1. Calculate the total number of bits in a day for a given data rate (same as the decimal system): $1 \text{ bps} \times 86400 \text{ seconds} = 86400 \text{ bits/day}$

2. Convert bits per day to Kibibits per day: $\frac{86400 \text{ bits}}{1024} \approx 84.375 \text{ Kibibits/day}$

So, in the binary system: $1 \text{ bits per second} \approx 84.375 \text{ Kibibits per day}$

Real-World Examples for Various Data Rates

1. Dial-Up Modem (56 Kbps):

   • Data Transfer Rate: $56,000 \text{ bps}$
   • Daily Data Transfer Volume: $\text{Base 10: } \frac{56,000 \times 86400}{1000} = 4838400 \text{ Kilobits/day} = 4,838.4 \text{ Megabits/day}$ $\text{Base 2: } \frac{56,000 \times 86400}{1024} \approx 4725.59 \text{ Kibibits/day} = 4.615 \text{ Mebibits/day}$

2. Standard Home Broadband (100 Mbps):

   • Data Transfer Rate: $100,000,000 \text{ bps}$
   • Daily Data Transfer Volume: $\text{Base 10: } \frac{100,000,000 \times 86400}{1000} = 8,640,000,000 \text{ Kilobits/day} = 8,640,000 \text{ Megabits/day} = 8,640 \text{ Gigabits/day}$ $\text{Base 2: } \frac{100,000,000 \times 86400}{1024} \approx 8,437,500 \text{ Kibibits/day} = 8,244.14 \text{ Mebibits/day} \approx 8.05 \text{ Gibibits/day}$

3. Gigabit Ethernet (1 Gbps):

   • Data Transfer Rate: $1,000,000,000 \text{ bps}$
   • Daily Data Transfer Volume: $\text{Base 10: } \frac{1,000,000,000 \times 86400}{1000} = 86,400,000,000 \text{ Kilobits/day} = 86,400,000 \text{ Megabits/day} = 86,400 \text{ Gigabits/day} = 86.4 \text{ Terabits/day}$ $\text{Base 2: } \frac{1,000,000,000 \times 86400}{1024} \approx 84,375,000 \text{ Kibibits/day} = 82,440.96 \text{ Mebibits/day} \approx 80.47 \text{ Gibibits/day}$

These examples illustrate the differences in data volumes when considering data rates over longer periods, taking into account the different base systems often used in measurements.