Question

Question: (I) Write the binary number 1010101010101010 as a decimal number.

Short answer

The decimal equivalent of 1010101010101010 is 43690.

Step-by-step solution

Understanding of digital electronics

Digital electronics is used to convert an analog signal voltage to a digital voltage in terms of binary codes. There are two possibilities for each bit, 0 and 1.

Given data

The binary number is 1010101010101010.

Determination of the decimal equivalent

The decimal equivalent of 01010101 is as follows,

\(\mathop 1\limits^{15} \mathop 0\limits^{14} \mathop 1\limits^{13} \mathop 0\limits^{12} \mathop 1\limits^{11} \mathop 0\limits^{10} \mathop 1\limits^9 \mathop 0\limits^8 \mathop 1\limits^7 \mathop 0\limits^6 \mathop 1\limits^5 \mathop 0\limits^4 \mathop 1\limits^3 \mathop 0\limits^2 \mathop 1\limits^1 \mathop 0\limits^0 \)

The decimal number equivalent is,

\(\begin{aligned}{c}{2^1} + {2^3} + {2^5} + {2^7} + {2^9} + {2^{11}} + {2^{13}} + {2^{15}}\\ &= 2 + 8 + 32 + 128 + 512 + 2048 + 8192 + 32768\\ &= 43690\end{aligned}\)

Thus, the decimal equivalent of 1010101010101010is 43690.