GB to MiB Converter

The Gigabyte is a decimal unit. It is defined as 1000^3 bytes, which equals 1000000000 bytes. Since 1 Byte = 8 bits, multiply the number of Bytes by 8 to express the value in bits.

$1\,\mathrm{GB} = 1,000^{3} \,\mathrm{B} \times 8\, = 8,000,000,000\,\mathrm{bit}$

The Mebibyte is a binary unit. It is defined as 1024^2 bytes, which equals 1048576 bytes. Since 1 Byte = 8 bits, multiply the number of Bytes by 8 to express the value in bits.

$1\,\mathrm{MiB} = 1,024^{2} \,\mathrm{B} \times 8\, = 8,388,608\,\mathrm{bit}$

One Gigabyte is equal to 8000000000 bits, while one Mebibyte equals 8388608 bits. The conversion factor is obtained by dividing the value of 1 source unit (in bits) by the value of 1 target unit (in bits).

$\dfrac{ 1\,\mathrm{GB} }{ 1\,\mathrm{MiB} } = \dfrac{ 8,000,000,000\,\mathrm{bit} }{ 8,388,608\,\mathrm{bit} } = \dfrac{ 8,000,000,000 }{ 8,388,608 }$

The fraction can be simplified by dividing both the numerator and denominator by 4,096, giving the exact conversion factor.

$\dfrac{ 8,000,000,000 }{ 8,388,608 } = \dfrac{ 8,000,000,000\div 4,096 }{ 8,388,608\div 4,096 } = \dfrac{ 1,953,125 }{ 2,048 }$

The exact factor is 1953125/2048. The decimal result is shown to 30 places or fewer when the division terminates earlier.

$\dfrac{ 1,953,125 }{ 2,048 } \approx 953.67431640625$

The conversion factor from Gigabyte (GB) to Mebibyte (MiB) is 953.67431640625. Therefore, any value in Gigabyte can be converted to Mebibyte by multiplying it by this factor.

$\boxed{ x\,\mathrm{GB} = x\times 953.67431640625\,\mathrm{MiB} }$

Multiply the number of Gigabytes by 953.67431640625 to obtain the equivalent value in Mebibytes.