Subjects computer science

Binary To Decimal Fd56Ad

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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**.