bits per second to Gigabytes per hour conversion

How to convert bits per second to gigabytes per hour?

Sure! Converting 1 bit per second (bps) to Gigabytes per hour (GB/hr) involves several steps, including unit conversions from seconds to hours and bits to gigabytes. Here's the step-by-step process for both base 10 (decimal) and base 2 (binary) systems:

Base 10 (Decimal) Conversion:

1. Convert bits to bytes: $1 \text{ bit} = \frac{1}{8} \text{ bytes} = 0.125 \text{ bytes/second}$

2. Convert seconds to hours: $1 \text{ second} = \frac{1}{3600} \text{ hours}$ So, in one hour, we have: $0.125 \text{ bytes/second} \times 3600 \text{ seconds/hour} = 450 \text{ bytes/hour}$

3. Convert bytes to gigabytes: $1 \text{ byte} = 1 \times 10^{-9} \text{ gigabytes}$ Therefore: $450 \text{ bytes/hour} \times 1 \times 10^{-9} \text{ gigabytes/byte} = 450 \times 10^{-9} \text{ gigabytes/hour} = 4.5 \times 10^{-7} \text{ gigabytes/hour}$

Base 2 (Binary) Conversion:

1. Convert bits to bytes (same as in Base 10): $1 \text{ bit} = \frac{1}{8} \text{ bytes} = 0.125 \text{ bytes/second}$

2. Convert seconds to hours (same as in Base 10): $0.125 \text{ bytes/second} \times 3600 \text{ seconds/hour} = 450 \text{ bytes/hour}$

3. Convert bytes to gibibytes (binary gigabytes): In the binary system, 1 gibibyte (GiB) = $2^{30}$ bytes: $1 \text{ byte} = \frac{1}{2^{30}} \text{ gibibytes} \approx 9.313 \times 10^{-10} \text{ gibibytes}$ Therefore: $450 \text{ bytes/hour} \times 9.313 \times 10^{-10} \text{ gibibytes/byte} \approx 4.19085 \times 10^{-7} \text{ gibibytes/hour}$

Real-World Examples

• Dial-Up Modem Speed: Typical dial-up modems operate at around 56,000 bps (56 kbps). Using the base 10 conversion: $56,000 \text{ bps} \approx 0.0252 \text{ GB/hr}$

• DSL Internet Speed: A typical DSL connection might have a speed of 10 Mbps (10,000,000 bps). Using the base 10 conversion: $10 \times 10^{6} \text{ bps} \approx 4.5 \text{ GB/hr}$

• Gigabit Ethernet: A standard gigabit Ethernet connection is 1 Gbps (1,000,000,000 bps). Using the base 10 conversion: $1 \times 10^{9} \text{ bps} \approx 450 \text{ GB/hr}$

By understanding these conversions and real-world examples, you can better grasp the differences and practical implications of varying data transfer rates.