Terabits to Gigabytes conversion

How to convert terabits to gigabytes?

Certainly! To convert terabits (Tb) to gigabytes (GB), we must consider the two different systems for measuring digital information: the base 10 (decimal) system and the base 2 (binary) system. Let's go through both:

Base 10 (Decimal System)

In the decimal system, 1 terabit (Tb) equals $10^{12}$ bits, and 1 gigabyte (GB) equals $10^9$ bytes.

Conversion Steps:

1. Convert terabits to bits: $1 \, \text{Tb} = 10^{12} \, \text{bits}$

2. Convert bits to bytes (since there are 8 bits in a byte): $10^{12} \, \text{bits} = \frac{10^{12}}{8} \, \text{bytes} = 125 \times 10^9 \, \text{bytes}$

3. Convert bytes to gigabytes: $125 \times 10^9 \, \text{bytes} = 125 \, \text{GB}$

So, in the base 10 (decimal) system: 1 Terabit (Tb) = 125 Gigabytes (GB)

Base 2 (Binary System)

In the binary system, 1 terabit (Tb) equals $2^{40}$ bits, and 1 gigabyte (GB) equals $2^{30}$ bytes.

Conversion Steps:

1. Convert terabits to bits: $1 \, \text{Tb} = 2^{40} \, \text{bits}$

2. Convert bits to bytes (since there are 8 bits in a byte): $2^{40} \, \text{bits} = \frac{2^{40}}{8} \, \text{bytes} = 2^{37} \, \text{bytes}$

3. Convert bytes to gigabytes: $2^{37} \, \text{bytes} = 2^{37} \, \text{bytes} \times \left(\frac{1 \, \text{GB}}{2^{30} \, \text{bytes}}\right) = 2^{7} \, \text{GB} = 128 \, \text{GB}$

So, in the base 2 (binary) system: 1 Terabit (Tb) = 128 Gigabytes (GB)

Real-World Examples for Other Quantities of Terabits

1. 100 Terabits:

   • Base 10: $100 \times 125$ GB = 12,500 GB
   • Base 2: $100 \times 128$ GB = 12,800 GB

2. 1 Petabit (Pb) (which is 1,000 Terabits):

   • Base 10: $1,000 \times 125$ GB = 125,000 GB
   • Base 2: $1,000 \times 128$ GB = 128,000 GB

3. 50 Terabits:

   • Base 10: $50 \times 125$ GB = 6,250 GB
   • Base 2: $50 \times 128$ GB = 6,400 GB

These conversions and examples demonstrate the difference between the base 10 and base 2 systems and how they affect the conversion of terabits to gigabytes.