The problem asks to convert binary numbers to their decimal equivalents. We are given a list of binary numbers and must find their decimal representation.

1. Problem Description

The problem asks to convert binary numbers to their decimal equivalents. We are given a list of binary numbers and must find their decimal representation.

2. Solution Steps

To convert a binary number to a decimal number, we multiply each digit of the binary number by $2$ raised to the power of its position (starting from 0 on the rightmost digit) and then sum the results.

Here are the solutions for each given binary number:

1. Binary = $1001$

Decimal = $(1 \times 2^3) + (0 \times 2^2) + (0 \times 2^1) + (1 \times 2^0) = 8 + 0 + 0 + 1 = 9$

2. Binary = $100000$

Decimal = $(1 \times 2^5) + (0 \times 2^4) + (0 \times 2^3) + (0 \times 2^2) + (0 \times 2^1) + (0 \times 2^0) = 32 + 0 + 0 + 0 + 0 + 0 = 32$

3. Binary = $1100101101$

Decimal = $(1 \times 2^9) + (1 \times 2^8) + (0 \times 2^7) + (0 \times 2^6) + (1 \times 2^5) + (0 \times 2^4) + (1 \times 2^3) + (1 \times 2^2) + (0 \times 2^1) + (1 \times 2^0) = 512 + 256 + 0 + 0 + 32 + 0 + 8 + 4 + 0 + 1 = 813$

4. Binary = $100001000$

Decimal = $(1 \times 2^8) + (0 \times 2^7) + (0 \times 2^6) + (0 \times 2^5) + (0 \times 2^4) + (1 \times 2^3) + (0 \times 2^2) + (0 \times 2^1) + (0 \times 2^0) = 256 + 0 + 0 + 0 + 0 + 8 + 0 + 0 + 0 = 264$

5. Binary = $10101001$

Decimal = $(1 \times 2^7) + (0 \times 2^6) + (1 \times 2^5) + (0 \times 2^4) + (1 \times 2^3) + (0 \times 2^2) + (0 \times 2^1) + (1 \times 2^0) = 128 + 0 + 32 + 0 + 8 + 0 + 0 + 1 = 169$

6. Binary = $1010000100$

Decimal = $(1 \times 2^9) + (0 \times 2^8) + (1 \times 2^7) + (0 \times 2^6) + (0 \times 2^5) + (0 \times 2^4) + (0 \times 2^3) + (1 \times 2^2) + (0 \times 2^1) + (0 \times 2^0) = 512 + 0 + 128 + 0 + 0 + 0 + 0 + 4 + 0 + 0 = 644$

7. Binary = $1011010111$

Decimal = $(1 \times 2^9) + (0 \times 2^8) + (1 \times 2^7) + (1 \times 2^6) + (0 \times 2^5) + (1 \times 2^4) + (0 \times 2^3) + (1 \times 2^2) + (1 \times 2^1) + (1 \times 2^0) = 512 + 0 + 128 + 64 + 0 + 16 + 0 + 4 + 2 + 1 = 727$

8. Binary = $1010101111$

Decimal = $(1 \times 2^9) + (0 \times 2^8) + (1 \times 2^7) + (0 \times 2^6) + (1 \times 2^5) + (0 \times 2^4) + (1 \times 2^3) + (1 \times 2^2) + (1 \times 2^1) + (1 \times 2^0) = 512 + 0 + 128 + 0 + 32 + 0 + 8 + 4 + 2 + 1 = 687$

9. Binary = $1101111110100$

Decimal = $(1 \times 2^{12}) + (1 \times 2^{11}) + (0 \times 2^{10}) + (1 \times 2^9) + (1 \times 2^8) + (1 \times 2^7) + (1 \times 2^6) + (1 \times 2^5) + (1 \times 2^4) + (0 \times 2^3) + (1 \times 2^2) + (0 \times 2^1) + (0 \times 2^0) = 4096 + 2048 + 0 + 512 + 256 + 128 + 64 + 32 + 16 + 0 + 4 + 0 + 0 = 7156$

1

0. Binary = $110110101111$

Decimal = $(1 \times 2^{11}) + (1 \times 2^{10}) + (0 \times 2^9) + (1 \times 2^8) + (1 \times 2^7) + (0 \times 2^6) + (1 \times 2^5) + (0 \times 2^4) + (1 \times 2^3) + (1 \times 2^2) + (1 \times 2^1) + (1 \times 2^0) = 2048 + 1024 + 0 + 256 + 128 + 0 + 32 + 0 + 8 + 4 + 2 + 1 = 3503$

3. Final Answer

1. 9

2. 32

3. 813

4. 264

5. 169

6. 644

7. 727

8. 687

9. 7156

1

0. 3503