Solve {l}{16^3*10+4*16+5*16^-1}{+16^-2}

$$\left. \begin{array}{l}{ 16 ^ { 3 } \times 10 + 4 \times 16 + 5 \times 16 ^ { - 1 } }\\{ + 16 ^ { - 2 } }\end{array} \right.$$

Sort

$$\frac{1}{256},\frac{656389}{16}$$

Solution Steps

Calculate 16 to the power of 3 and get 4096.

$$sort(4096\times 10+4\times 16+5\times 16^{-1},16^{-2})$$

Multiply 4096 and 10 to get 40960.

$$sort(40960+4\times 16+5\times 16^{-1},16^{-2})$$

Multiply 4 and 16 to get 64.

$$sort(40960+64+5\times 16^{-1},16^{-2})$$

Add 40960 and 64 to get 41024.

$$sort(41024+5\times 16^{-1},16^{-2})$$

Calculate 16 to the power of -1 and get \frac{1}{16}.

$$sort(41024+5\times \frac{1}{16},16^{-2})$$

Multiply 5 and \frac{1}{16} to get \frac{5}{16}.

$$sort(41024+\frac{5}{16},16^{-2})$$

Add 41024 and \frac{5}{16} to get \frac{656389}{16}.

$$sort(\frac{656389}{16},16^{-2})$$

Calculate 16 to the power of -2 and get \frac{1}{256}.

$$sort(\frac{656389}{16},\frac{1}{256})$$

Least common denominator of the numbers in the list \frac{656389}{16},\frac{1}{256} is 256. Convert numbers in the list to fractions with denominator 256.

$$\frac{10502224}{256},\frac{1}{256}$$

To sort the list, start from a single element \frac{10502224}{256}.

$$\frac{10502224}{256}$$

Insert \frac{1}{256} to the appropriate location in the new list.

$$\frac{1}{256},\frac{10502224}{256}$$

Replace the obtained fractions with the initial values.

$$\frac{1}{256},\frac{656389}{16}$$

Evaluate

$$\frac{656389}{16},\ \frac{1}{256}$$