Question

Translate $\mathbf{0}\mathbf{\times }\mathit{a}\mathit{b}\mathit{c}\mathit{d}\mathit{e}\mathit{f}\mathbf{12}$into decimal

Short answer

The translation is:

2882400018

Step-by-step solution

Define Hexadecimal

Hexadecimal is the base 16 number system that represents the 4-bit binary numbers in a simplified way. In hexadecimal the values from 10-15 is represented by the alphabets A-F.

In machine programs, most values will be considered in a hexadecimal format which makes the execution faster.

Determine the decimal value

For the given value, the decimal value can be calculated by multiplying each term by the powers of 16 and summing all values.

The calculation is as follows:

$0\times abcdef12=\left(2\times {16}^0\right)+\left(1\times {16}^1\right)+\left(15\times {16}^2\right)+\left(14\times {16}^3\right)+\left(13\times {16}^4\right)+\left(12\times {16}^5\right)+\left(11\times {16}^6\right)+\left(10\times {16}^7\right)$

The decimal value of $0\times abcdef12$is 2882400018