Convert bit to word
Learn how to convert
1
bit to
word
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(bit\right)={\color{rgb(20,165,174)} x}\left(word\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(byte\right)\)
\(\text{Left side: 1.0 } \left(bit\right) = {\color{rgb(89,182,91)} \dfrac{1.0}{8.0}\left(byte\right)} = {\color{rgb(89,182,91)} \dfrac{1.0}{8.0}\left(B\right)}\)
\(\text{Right side: 1.0 } \left(word\right) = {\color{rgb(125,164,120)} 2.0\left(byte\right)} = {\color{rgb(125,164,120)} 2.0\left(B\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(bit\right)={\color{rgb(20,165,174)} x}\left(word\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{1.0}{8.0}} \times {\color{rgb(89,182,91)} \left(byte\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 2.0}} \times {\color{rgb(125,164,120)} \left(byte\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} \dfrac{1.0}{8.0}} \cdot {\color{rgb(89,182,91)} \left(B\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 2.0} \cdot {\color{rgb(125,164,120)} \left(B\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{1.0}{8.0}} \cdot {\color{rgb(89,182,91)} \cancel{\left(B\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 2.0} \times {\color{rgb(125,164,120)} \cancel{\left(B\right)}}\)
\(\text{Conversion Equation}\)
\(\dfrac{1.0}{8.0} = {\color{rgb(20,165,174)} x} \times 2.0\)
Switch sides
\({\color{rgb(20,165,174)} x} \times 2.0 = \dfrac{1.0}{8.0}\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{1.0}{2.0}\right)\)
\({\color{rgb(20,165,174)} x} \times 2.0 \times \dfrac{1.0}{2.0} = \dfrac{1.0}{8.0} \times \dfrac{1.0}{2.0}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{2.0}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{2.0}}} = \dfrac{1.0 \times 1.0}{8.0 \times 2.0}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{1.0}{8.0 \times 2.0}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x} = 0.0625 = 6.25 \times 10^{-2}\)
\(\text{Conversion Equation}\)
\(1.0\left(bit\right) = {\color{rgb(20,165,174)} 6.25 \times 10^{-2}}\left(word\right)\)
