Binary To Decimal Fd56Ad
1. The problem asks to convert the binary number 1011 1010 0100 0011 to its decimal equivalent treating it as a 16-bit unsigned value.
2. The binary number is 16 bits long: 1011101001000011.
3. To convert a binary number to decimal, use the formula:
$$\text{Decimal} = \sum_{i=0}^{n-1} b_i \times 2^i$$
where $b_i$ is the bit at position $i$ (starting from 0 at the right).
4. Write the binary number without spaces: 1011101001000011.
5. Assign powers of 2 from right to left:
$$\begin{aligned}
&1 \times 2^{15} + 0 \times 2^{14} + 1 \times 2^{13} + 1 \times 2^{12} + 1 \times 2^{11} + 0 \times 2^{10} + 1 \times 2^9 + 0 \times 2^8 \\
&+ 0 \times 2^7 + 1 \times 2^6 + 0 \times 2^5 + 0 \times 2^4 + 0 \times 2^3 + 0 \times 2^2 + 1 \times 2^1 + 1 \times 2^0
\end{aligned}$$
6. Calculate each term:
$$\begin{aligned}
&1 \times 32768 + 0 + 1 \times 8192 + 1 \times 4096 + 1 \times 2048 + 0 + 1 \times 512 + 0 \\
&+ 0 + 1 \times 64 + 0 + 0 + 0 + 0 + 1 \times 2 + 1 \times 1
\end{aligned}$$
7. Sum all values:
$$32768 + 8192 + 4096 + 2048 + 512 + 64 + 2 + 1 = 47883$$
8. Therefore, the decimal equivalent of the 16-bit unsigned binary number 1011101001000011 is **47883**.