Thinking Mathematically (6th Edition)

Published by Pearson

Chapter 4 - Number Representation and Calculation - 4.3 Computation in Positional Systems - Exercise Set 4.3: 21

Answer

$10_{two}$

Work Step by Step

Start with the right-most column. $1-1=0$ Record: $0_{two}$ $\begin{array}{lllll} & 1 & 0 & 0 & 1_{two}\\ - & & 1 & 1 & 1_{two}\\ -- & -- & -- & -- &-- \\ & & & & 0_{two} \end{array}$ Next column: $0$ is less than $1$... borrow 1 $two$ from the $10_{two},$ because we can't borrow from zero. $(0+2)-1=1$ Record the $1.$ $\begin{array}{lllll} & 1 & 0 & 0 & 1_{two}\\ - & & 1 & 1 & 1_{two}\\ -- & -- & -- & -- &-- \\ & & & 1 & 0_{two} \end{array}$ We are left with $10_{two}-1_{two}$, but since we borrowed a two from the previous column, the remaining subtraction is $1_{two}-1_{two}=0$, which we do not record. Result: $10_{two}$

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