bits per day to Kibibits per hour conversion

How to convert bits per day to kibibits per hour?

Sure, let's walk through the conversion of 1 bit per day to Kibibits per hour, and we'll explore both the base 10 (SI) and base 2 (binary) systems.

Base 2 (Binary System)

1. Bits per day to Bits per hour:

   • There are 24 hours in a day.
   • So, $1 \text{ bit/day} = \frac{1 \text{ bit}}{24 \text{ hours}}$ = $0.041667 \text{ bits/hour}$.

2. Bits per hour to Kibibits per hour:

   • There are 1024 bits in 1 Kibibit (Ki).
   • So, $0.041667 \text{ bits/hour} \times \frac{1 \text{ Kibibit}}{1024 \text{ bits}}$ ≈ $4.069 \times 10^{-5} \text{ Kibibits/hour}$.

Base 10 (SI System)

1. Bits per day to Bits per hour:

   • There are 24 hours in a day.
   • So, $1 \text{ bit/day} = \frac{1 \text{ bit}}{24 \text{ hours}}$ = $0.041667 \text{ bits/hour}$.

2. Bits per hour to Kilobits per hour:

   • There are 1000 bits in 1 Kilobit (Kbit).
   • So, $0.041667 \text{ bits/hour} \times \frac{1 \text{ Kilobit}}{1000 \text{ bits}}$ = $4.167 \times 10^{-5} \text{ Kilobits/hour}$.

Summary

• Binary System: ~ $4.069 \times 10^{-5} \text{ Kibibits/hour}$
• SI System: ~ $4.167 \times 10^{-5} \text{ Kilobits/hour}$

Real-world Examples

Let's explore some other data transfer rates in bits per day and their conversions:

Common Historical Examples:

1. Morse Code Telegraph (circa 1840)

   • Speed: ~5 words per minute.
   • Each word is ~5 characters, and each character is ~5 bits (including spaces).
   • Daily transfer: $5 \text{ words/min} \times 5 \text{ chars/word} \times 5 \text{ bits/char} \times 60 \text{ min/hr} \times 24 \text{ hr/day} = 180,000 \text{ bits/day}$.
   • Converted to Kibibits per hour: $\text{180,000 bits/day} \times \frac{1 \text{ Kibibit}}{1024 \text{ bits}} \times \frac{1}{24 \text{ hours}} ≈ 7.324 \text{ Kibibits/hour}$.

2. Early Dial-up Internet (14.4 kbit/s modem)

   • Speed: 14,400 bits/second.
   • Daily transfer: $14,400 \text{ bits/sec} \times 60 \text{ sec/min} \times 60 \text{ min/hr} \times 24 \text{ hr/day} = 1,244,160,000 \text{ bits/day}$.
   • Converted to Kibibits per hour: $\text{1,244,160,000 bits/day} \times \frac{1 \text{ Kibibit}}{1024 \text{ bits}} \times \frac{1}{24 \text{ hours}} ≈ 50,955.078 \text{ Kibibits/hour}$.

3. Modern Fiber Optic Connection (1 Gbits/s)

   • Speed: 1,000,000,000 bits/second.
   • Daily transfer: $1,000,000,000 \text{ bits/sec} \times 60 \text{ sec/min} \times 60 \text{ min/hr} \times 24 \text{ hr/day} = 86,400,000,000,000 \text{ bits/day}$.
   • Converted to Kibibits per hour: $\text{86,400,000,000,000 bits/day} \times \frac{1 \text{ Kibibit}}{1024 \text{ bits}} \times \frac{1}{24 \text{ hours}} ≈ 3,422,851,562.5 \text{ Kibibits/hour}$.

These examples illustrate the dramatic increase in data transfer rates from historical to modern times and offer a perspective on how bits per day translates to more common units of data transfer, especially in computing and telecommunications contexts.