Terabits per hour to Bytes per day conversion

How to convert terabits per hour to bytes per day?

To convert 1 Terabit per hour (Tb/h) to Bytes per day, you need to follow these steps. We'll perform the calculations for both the base 10 (decimal) and base 2 (binary) systems.

Base 10 (Decimal) Calculations

1. Convert Terabits to bits:

   • 1 Terabit (Tb) = $10^{12}$ bits

2. Convert bits to Bytes:

   • 1 Byte (B) = 8 bits
   • Therefore, $10^{12}$ bits = $\frac{10^{12}}{8} = 1.25 \times 10^{11}$ Bytes

3. Convert Bytes per hour to Bytes per day:

   • 1 day = 24 hours
   • Therefore, $1.25 \times 10^{11}$ Bytes/hour $\times 24$ hours/day = $3 \times 10^{12}$ Bytes/day

So, in the base 10 (decimal) system, 1 Terabit per hour is equivalent to $3 \times 10^{12}$ Bytes per day.

Base 2 (Binary) Calculations

1. Convert Terabits to bits:

   • 1 Terabit (Tb) = $2^{40}$ bits

2. Convert bits to Bytes:

   • 1 Byte (B) = 8 bits
   • Therefore, $2^{40}$ bits = $\frac{2^{40}}{8} = 2^{37}$ Bytes

3. Convert Bytes per hour to Bytes per day:

   • 1 day = 24 hours
   • Therefore, $2^{37}$ Bytes/hour $\times 24$ hours/day = $24 \times 2^{37} = 3 \times 2^{37}$ Bytes/day

So, in the base 2 (binary) system, 1 Terabit per hour is equivalent to $3 \times 2^{37}$ Bytes per day, which is approximately $3.94 \times 10^{12}$ Bytes per day.

Real-World Examples for Other Quantities of Terabits per Hour

1. 5 Terabits per hour (5 Tb/h):

   • Base 10:
     • Bits: $5 \times 10^{12}$
     • Bytes/hour = $\frac{5 \times 10^{12}}{8}$ = $6.25 \times 10^{11}$
     • Bytes/day = $6.25 \times 10^{11} \times 24 = 1.5 \times 10^{13}$ Bytes
   • Base 2:
     • Bits: $5 \times 2^{40}$
     • Bytes/hour = $\frac{5 \times 2^{40}}{8}$ = $5 \times 2^{37}$
     • Bytes/day = $5 \times 24 \times 2^{37} = 120 \times 2^{37}$

2. 0.5 Terabits per hour (0.5 Tb/h):

   • Base 10:
     • Bits: $0.5 \times 10^{12}$
     • Bytes/hour = $\frac{0.5 \times 10^{12}}{8}$ = $6.25 \times 10^{10}$
     • Bytes/day = $6.25 \times 10^{10} \times 24 = 1.5 \times 10^{12}$ Bytes
   • Base 2:
     • Bits: $0.5 \times 2^{40}$
     • Bytes/hour = $\frac{0.5 \times 2^{40}}{8}$ = $0.5 \times 2^{37}$
     • Bytes/day = $0.5 \times 24 \times 2^{37} = 12 \times 2^{37}$

3. 50 Terabits per hour (50 Tb/h):

   • Base 10:
     • Bits: $50 \times 10^{12}$
     • Bytes/hour = $\frac{50 \times 10^{12}}{8}$ = $6.25 \times 10^{12}$
     • Bytes/day = $6.25 \times 10^{12} \times 24 = 1.5 \times 10^{14}$ Bytes
   • Base 2:
     • Bits: $50 \times 2^{40}$
     • Bytes/hour = $\frac{50 \times 2^{40}}{8}$ = $50 \times 2^{37}$
     • Bytes/day = $50 \times 24 \times 2^{37} = 1200 \times 2^{37}$

These calculations provide a concrete idea of how data transfer rates in Terabits per hour translate to Bytes per day in both base 10 and base 2 systems.