Numbering System Problem Solved
Numbering System Problem Solved Problem Carry out the following conversions:a) 1238 to the binary system.B) 10101012 to the octal system.C) BACA16 to the binary system.D) 10101012 to the hexadecimal system.E) 1316310 to the binary system.Sug. Use successive divisions and polynomial decomposition. T. Solution We present 2 ways to solve this problem. A) First Way: Let's say that this is the trivial way to carry out this process. We convert the number 1238 to a number in base 10 (the one we use), through the polynomial decomposition of the following form:\( 123_8 = 1 \times 8^2 + 2\times 8^1 + 3 \times 8^0 \)\( \rightarrow 1 \times 64 + 2\times 8 + 3 \times 1 \ \rightarrow 83\)Then we convert the number 83 to a number in base 2 (binary) through successiv divisions: We proceed to write the numbers that are enclosed in a square, starting with the number that is on the left side and ending with the one on the right side, thus obtaining the number in base 2, that is:\( 83 = ...