bits per hour to Terabits per day conversion

How to convert bits per hour to terabits per day?

To convert bits per hour to Terabits per day, we need to follow a couple of conversion steps:

1. Convert bits per hour to bits per day
2. Convert bits per day to Terabits per day

Let's break this down in both base 10 and base 2 systems.

Base 10 (Decimal)

Step 1: Convert bits per hour to bits per day

There are 24 hours in a day. Therefore, $1 \text{ bit per hour} = 1 \times 24 = 24 \text{ bits per day}$

Step 2: Convert bits per day to Terabits per day

In the decimal system (base 10), 1 Terabit (Tb) = $10^{12}$ bits.

$24 \text{ bits per day} = \frac{24}{10^{12}} \text{ Terabits per day} = 2.4 \times 10^{-11} \text{ Terabits per day}$

Base 2 (Binary)

Step 1: Convert bits per hour to bits per day

Again, there are 24 hours in a day. $1 \text{ bit per hour} = 1 \times 24 = 24 \text{ bits per day}$

Step 2: Convert bits per day to Terabits per day

In the binary system (base 2), 1 Tebibit (Tib) = $2^{40}$ bits. Note: Binary prefixes use a different naming convention (Tebibit instead of Terabit).

$24 \text{ bits per day} = \frac{24}{2^{40}} \text{ Tebibits per day} = \frac{24}{1,099,511,627,776} \text{ Tebibits per day} \approx 2.18 \times 10^{-11} \text{ Tebibits per day}$

Real World Examples

Example 1: Internet Usage

• Slow Dial-Up Connection: An old dial-up internet connection could transfer data at about 56,000 bits per second. Over an hour, this would be $56,000 \times 3600 = 201,600,000$ bits. Converted to Terabits per day in the base 10 system, it would be approximately $\frac{201,600,000 \times 24}{10^{12}} \approx 4.8384 \times 10^{-3}$ Tb/day.

Example 2: Modern Fiber Optic Connection

• Fast Fiber Optic Connection: A modern fiber optic internet connection could transfer data at 1 Gbps (1 billion bits per second). Over an hour, this would be $1,000,000,000 \times 3600 = 3.6 \times 10^{12}$ bits. Converted to Terabits per day in the base 10 system, it would be $\frac{3.6 \times 10^{12} \times 24}{10^{12}} = 86.4$ Tb/day.

By understanding these conversion steps and real-world examples, you gain insight into how various scales of data transfer rates relate to each other, whether in traditional base 10 or binary base 2 systems.