Question

Convert $(7206{)}_8\mathrm{and}(\mathrm{A}0\mathrm{EB}{)}_{16}$to a binary representation

Short answer

$(111010000110{)}_2$

$(1010000011101011{)}_2$

Step-by-step solution

Step 1

$$\begin{gathered} (7206{)}_8=7\ast 8^3+2\ast 8^2+6\ast 8^0 \\ =\left(2^2+2^1+2^0\right)2^9+2^1\ast 2^6+\left(2^2+2^1\right)2^0 \\ =2^{11}+2^{10}+2^9+2^7+2^2+2^1 \\ =(111010000110{)}_2 \end{gathered}$$

Step 2

$$\begin{gathered} (\mathrm{A}0\mathrm{EB}{)}_{16}=10\ast {16}^3+{14}^{\ast }{16}^1+{11}^{\ast }{16}^0 \\ =\left(2^3+2^1\right)2^{1}2+\left(2^3+2^2+2^1\right)2^4+\left(2^3+2^1+2^0\right)2^0 \\ =2^{15}+2^{13}+2^6+2^5+2^3+2^1+2^0 \\ =(1010000011101011{)}_2 \end{gathered}$$