bits per day to Gigabytes per second conversion

How to convert bits per day to gigabytes per second?

To convert 1 bit per day to Gigabytes per second, you need to consider two aspects: conversion of time units and data units. First, let's break it down step by step.

Step 1: Time Conversion

1 day = 24 hours 1 hour = 60 minutes 1 minute = 60 seconds

So, 1 day = 24 * 60 * 60 = 86,400 seconds

Step 2: Data Conversion

1 bit = $1 / 8$ bytes 1 byte = $1 / 1,000,000,000$ gigabytes (GB) in base 10 (decimal system) 1 byte = $1 / 1,073,741,824$ gibibytes (GiB) in base 2 (binary system, often called "GB" in some contexts)

Step 3: Combine Time and Data Conversions

For Base 10 (Decimal System):

1 bit/day = 1 bit / 86,400 seconds

Convert bits to bytes: 1 bit / 86,400 seconds * 1 byte / 8 bits = 1 / (86,400 * 8) bytes/second 1 byte = $1 / 1,000,000,000$ gigabytes (GB)

So, $\frac{1}{86,400 \times 8} \text{ bytes/second} = \frac{1}{691,200} \text{ bytes/second}$

Convert to gigabytes: $\frac{1}{691,200} \text{ bytes/second} \times \frac{1 \text{ GB}}{1,000,000,000 \text{ bytes}} = \frac{1}{691,200,000,000} \text{ GB/second}$

For Base 2 (Binary System):

1 bit/day = 1 bit / 86,400 seconds

Convert bits to bytes: 1 bit / 86,400 seconds * 1 byte / 8 bits = 1 / (86,400 * 8) bytes/second 1 byte = $1 / 1,073,741,824$ gibibytes (GiB)

So, $\frac{1}{86,400 \times 8} \text{ bytes/second} = \frac{1}{691,200} \text{ bytes/second}$

Convert to gibibytes: $\frac{1}{691,200} \text{ bytes/second} \times \frac{1 \text{ GiB}}{1,073,741,824 \text{ bytes}} = \frac{1}{741,455,616,000} \text{ GiB/second}$

Summary:

• In base 10 (decimal system), $1$ bit per day is equivalent to $\frac{1}{691,200,000,000}$ GB/second.
• In base 2 (binary system), $1$ bit per day is equivalent to $\frac{1}{741,455,616,000}$ GiB/second.

Real-World Examples:

To give context to these conversions, let's look at some other quantities of bits per day:

1 Megabit per day (1,000,000 bits/day) to Gigabytes per second:

• Base 10: $\frac{1,000,000}{691,200,000,000} \approx 1.4459 \times 10^{-6}$ GB/second
• Base 2: $\frac{1,000,000}{741,455,616,000} \approx 1.3492 \times 10^{-6}$ GiB/second

1 Gigabit per day (1,000,000,000 bits/day) to Gigabytes per second:

• Base 10: $\frac{1,000,000,000}{691,200,000,000} \approx 1.4459 \times 10^{-3}$ GB/second
• Base 2: $\frac{1,000,000,000}{741,455,616,000} \approx 1.3492 \times 10^{-3}$ GiB/second

So, if you had a modest internet-connected device that transferred 1 megabit per day, its data rate in base 10 would be approximately 1.4459 micro-GB per second, which is extremely small compared to modern network speeds. Similarly, for larger data rates, the conversions show how imperceptibly slow data transfers can be over long timescales compared to the high-speed data rates we're accustomed to.