Chapter 4 - Number Representation and Calculation - 4.3 Computation in Positional Systems - Exercise Set 4.3 - Page 234: 11

$23536_{seven}$

Work Step by Step

Rightmost column: $2+4=6=6\times 1=6_{seven}$ record the $6$, no carry, $\left[\begin{array}{llllll} & & & & & \\ & 1 & 4 & 6 & 3 & 2_{seven}\\ + & & 5 & 6 & 0 & 4_{seven}\\ & - & - & - & - & -\\ & & & & & 6_{seven} \end{array}\right.$ Next column: $3+0=3\times 1=3_{seven}$ record the $3$, no carry, $\left[\begin{array}{llllll} & & & & & \\ & 1 & 4 & 6 & 3 & 2_{seven}\\ + & & 5 & 6 & 0 & 4_{seven}\\ & - & - & - & - & -\\ & & & & 3 & 6_{seven} \end{array}\right.$ Next column: $6+6=12=1\times 7+5\times 1=15_{seven}$ record the $5$, carry the 1, $\left[\begin{array}{llllll} & & 1 & & & \\ & 1 & 4 & 6 & 3 & 2_{seven}\\ + & & 5 & 6 & 0 & 4_{seven}\\ & - & - & - & - & -\\ & & & 5 & 3 & 6_{seven} \end{array}\right.$ Next column: $1+4+5=10=1\times 7+3\times 1=13_{seven}$ record the $3$, carry the 1, $\left[\begin{array}{llllll} & 1 & 1 & & & \\ & 1 & 4 & 6 & 3 & 2_{seven}\\ + & & 5 & 6 & 0 & 4_{seven}\\ & - & - & - & - & -\\ & & 3 & 5 & 3 & 6_{seven} \end{array}\right.$ Last column: $1+1=2=2_{seven}$ Record the 2 Result: $23536_{seven}$

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