To convert binary numbers to decimal, follow these steps:
### Converting \(1110111100_{2}\) to Decimal
Binary numbers are based on powers of 2, so we can convert them to decimal by multiplying each digit by \(2\) raised to the power of its position, counting from right to left starting with position 0.
Step-by-step conversion:
1. Write down the binary number and assign powers of 2 to each position, starting from the right:
[tex]\[
1 \cdot 2^9 + 1 \cdot 2^8 + 1 \cdot 2^7 + 0 \cdot 2^6 + 1 \cdot 2^5 + 1 \cdot 2^4 + 1 \cdot 2^3 + 1 \cdot 2^2 + 0 \cdot 2^1 + 0 \cdot 2^0
\][/tex]
2. Calculate the value of each term:
[tex]\[
1 \cdot 512 + 1 \cdot 256 + 1 \cdot 128 + 0 \cdot 64 + 1 \cdot 32 + 1 \cdot 16 + 1 \cdot 8 + 1 \cdot 4 + 0 \cdot 2 + 0 \cdot 1
\][/tex]
3. Simplify and sum these values:
[tex]\[
512 + 256 + 128 + 0 + 32 + 16 + 8 + 4 + 0 + 0 = 956
\][/tex]
Therefore, \(1110111100_{2}\) converts to \(956_{10}\).
### Converting \(10101010_{2}\) to Decimal
Similarly, we convert this binary number by the same method:
Step-by-step conversion:
1. Write down the binary number and assign powers of 2 to each position:
[tex]\[
1 \cdot 2^7 + 0 \cdot 2^6 + 1 \cdot 2^5 + 0 \cdot 2^4 + 1 \cdot 2^3 + 0 \cdot 2^2 + 1 \cdot 2^1 + 0 \cdot 2^0
\][/tex]
2. Calculate the value of each term:
[tex]\[
1 \cdot 128 + 0 \cdot 64 + 1 \cdot 32 + 0 \cdot 16 + 1 \cdot 8 + 0 \cdot 4 + 1 \cdot 2 + 0 \cdot 1
\][/tex]
3. Simplify and sum these values:
[tex]\[
128 + 0 + 32 + 0 + 8 + 0 + 2 + 0 = 170
\][/tex]
Therefore, \(10101010_{2}\) converts to \(170_{10}\).
### Summary
- The binary number \(1110111100_{2}\) converts to \(956_{10}\).
- The binary number [tex]\(10101010_{2}\)[/tex] converts to [tex]\(170_{10}\)[/tex].
