To convert the hexadecimal number [tex]\(BE_{16}\)[/tex] to a decimal (base 10) number, we will follow these steps:
1. Identify the positions of the digits:
- In hexadecimal, each digit represents a power of 16. The rightmost digit is in the [tex]\(16^0\)[/tex] position, the next one to the left is in the [tex]\(16^1\)[/tex] position, and so on.
- For [tex]\(BE_{16}\)[/tex]: [tex]\(B\)[/tex] is in the [tex]\(16^1\)[/tex] position, and [tex]\(E\)[/tex] is in the [tex]\(16^0\)[/tex] position.
2. Convert hexadecimal digits to decimal equivalents:
- In the hexadecimal system, [tex]\(B\)[/tex] represents 11 and [tex]\(E\)[/tex] represents 14 in the decimal system.
3. Calculate the value of each position:
- Position [tex]\(16^1\)[/tex] (for digit B): [tex]\(11 \times 16^1 = 11 \times 16 = 176\)[/tex]
- Position [tex]\(16^0\)[/tex] (for digit E): [tex]\(14 \times 16^0 = 14 \times 1 = 14\)[/tex]
4. Sum the values:
- Combine these values to get the decimal equivalent: [tex]\(176 + 14 = 190\)[/tex]
Therefore, the hexadecimal number [tex]\(BE_{16}\)[/tex] converts to the decimal number [tex]\(190_{10}\)[/tex].
