## Thinking Mathematically (6th Edition)

Published by Pearson

# Chapter 4 - Number Representation and Calculation - 4.3 Computation in Positional Systems - Exercise Set 4.3 - Page 234: 4

#### Answer

$1000_{two}$

#### Work Step by Step

Rightmost column: $1+1=2=1\times 2+0\times 1=_{}10_{two}$ record the $0$( carry the 1): $.\qquad \quad\$1 $.\qquad \$1 0 $1_{two}$ $.\quad +\ \ \ \ \$1 $1_{two}$ $.\quad \quad \_\_\_\_$ $.\qquad \quad \ \ 0_{two}$ Next column: $1+0+1=2=1\times 2+0\times 1=_{}10_{two}$ record the $0$( carry the 1): $.\qquad\ 1\$1 $.\qquad\$1 0 $1_{two}$ $.\quad +\ \ \ \ \$1 $1_{two}$ $.\quad \quad \_\_\_\_$ $.\qquad\quad 0 \ 0_{two}$ Next column: $1+1=2=1\times 2+0\times 1=_{}10_{two}$ record the $10$ $.\qquad\ 1\$1 $.\qquad\$1 0 $1_{two}$ $.\quad +\ \ \ \ \$1 $1_{two}$ $.\quad \quad \_\_\_\_$ $.\quad\ 1\ 0\ 0 \ 0_{two}$ Check in base 10: 5+3=8

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