Convert the decimal number [latex] (231)_{10} [/latex] into its binary equivalent.

[latex] \begin{array}{lll} 231=115 \times 2+1 & N_0=115 & a_0=1 \\ 115=57 \times 2+1 & N_1=57 & a_1=1 \\ 57=28 \times 2+1 & N_2=28 & a_2=1 \\ 28=14 \times 2+0 & N_3=14 & a_3=0 \\ 14=7 \times 2+0 & N_4=7 & a_4=0 \\ 7=3 \times 2+1 & N_5=3 & a_5=1 \\ 3=1 \times 2+1 & N_6=1 & a_6=1 \\ 1=0 \times 2+1 & N_7=0 & a_7=1 \end{array} [/latex] Thus the binary representation of the decimal number [latex] (231)_{10} \text { is }(11100111)_2 [/latex]. It can be computed from the expression [latex] \left(a_n a_{n-1} \ldots a_1 a_0\right)_2 [/latex].

Question 1.4: Convert the decimal number (231)10 into its binary equivalen...

Numerical Methods: Fundamentals and Applications

Convert the decimal number $(231)_{10}$ into its binary equivalent.

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$\begin{array}{lll} 231=115 \times 2+1 & N_0=115 & a_0=1 \\ 115=57 \times 2+1 & N_1=57 & a_1=1 \\ 57=28 \times 2+1 & N_2=28 & a_2=1 \\ 28=14 \times 2+0 & N_3=14 & a_3=0 \\ 14=7 \times 2+0 & N_4=7 & a_4=0 \\ 7=3 \times 2+1 & N_5=3 & a_5=1 \\ 3=1 \times 2+1 & N_6=1 & a_6=1 \\ 1=0 \times 2+1 & N_7=0 & a_7=1 \end{array}$

Thus the binary representation of the decimal number $(231)_{10} \text { is }(11100111)_2$ . It can be computed from the expression $\left(a_n a_{n-1} \ldots a_1 a_0\right)_2$ .