MathDB
The Binary System

Source:

June 8, 2009

Problem Statement

The base of the decimal number system is ten, meaning, for example, that 123 \equal{} 1\cdot 10^2 \plus{} 2\cdot 10 \plus{} 3. In the binary system, which has base two, the first five positive integers are 1,10,11,100,101 1,\,10,\,11,\,100,\,101. The numeral 10011 10011 in the binary system would then be written in the decimal system as: <spanclass=latexbold>(A)</span> 19<spanclass=latexbold>(B)</span> 40<spanclass=latexbold>(C)</span> 10011<spanclass=latexbold>(D)</span> 11<spanclass=latexbold>(E)</span> 7 <span class='latex-bold'>(A)</span>\ 19 \qquad <span class='latex-bold'>(B)</span>\ 40\qquad <span class='latex-bold'>(C)</span>\ 10011\qquad <span class='latex-bold'>(D)</span>\ 11\qquad <span class='latex-bold'>(E)</span>\ 7