compsci-gb-vs-gib.html
            
                
                    
                        
                        * created: 2025-10-06T19:02
                        
                         
                        * modified: 2025-10-06T19:06
                        
                        
                    
                
                title
                Difference between Giga- and Gibibyte
                description
                Description
                
             
            GiB vs GB
GibiByte (GiB) are based on base 2 and reflect the capacity more accurately (generally speaking).
\begin{align}
4\ \text{GiB} &= 4 \times 2^{10}\ \text{MiB} \\
&= 4 \times 1{,}024\ \text{MiB} \\
&= 4{,}096\ \text{MiB} \\
\\ 
&= 4 \times 2^{10} \times 2^{10}\ \text{KiB} \\
&= 4 \times 1{,}024 \times 1{,}024\ \text{KiB} \\
&= 4{,}194{,}304\ \text{KiB} \\
\\ 
&= 4 \times 2^{10} \times 2^{10} \times 2^{10}\ \text{Byte} \\
&= 4 \times 1{,}024 \times 1{,}024 \times 1{,}024\ \text{Byte} \\
&= 4{,}294{,}967{,}296\ \text{Byte} \\
\\ 
&= 4 \times 2^{10} \times 2^{10} \times 2^{10} \times 8\ \text{bit} \\
&= 4 \times 1{,}024 \times 1{,}024 \times 1{,}024 \times 8\ \text{bit} \\
&= 34{,}359{,}738{,}368\ \text{bit}
\end{align}
GigaByte (GB) are based on base 10 and are often used for simplicity (easier to reason with).
\begin{align}
4\ \text{GB} &= 4 \times 10^{3}\ \text{MB} \\
&= 4 \times 1{,}000\ \text{MB} \\
&= 4{,}000\ \text{MB} \\[10pt]
\\
&= 4 \times 10^{3} \times 10^{3}\ \text{KB} \\
&= 4 \times 1{,}000 \times 1{,}000\ \text{KB} \\
&= 4{,}000{,}000\ \text{KB} \\
\\
&= 4 \times 10^{3} \times 10^{3} \times 10^{3}\ \text{Byte} \\
&= 4 \times 1{,}000 \times 1{,}000 \times 1{,}000\ \text{Byte} \\
&= 4{,}000{,}000{,}000\ \text{Byte} \\
\\
&= 4 \times 10^{3} \times 10^{3} \times 10^{3} \times 8\ \text{bit} \\
&= 4 \times 1{,}000 \times 1{,}000 \times 1{,}000 \times 8\ \text{bit} \\
&= 32{,}000{,}000{,}000\ \text{bit}
\end{align}