Below is a regular binary number:

11100110

Please write it’s base 10 value (e.g 14, 28, 183) in the space provided.

Question

Below is a regular binary number:

11100110

Please write it’s base 10 value (e.g 14, 28, 183) in the space provided.

BlackTom AI · Accepted Answer

Binary positional values are powers of two, so each 1-bit contributes 2^position where the rightmost bit is position 0.

1. Relevant knowledge points and concepts
- Binary (base-2) uses digits 0 and 1.
- Each digit at position n (counting from right, starting at 0) has weight 2^n.
- To convert to decimal, multiply each bit by its weight and sum the results.

2. Step-by-step reasoning process
Write the binary number with positions under each bit:
bits:  1  1  1  0  0  1  1  0
index: 7  6  5  4  3  2  1  0
Compute the value contributed by each 1-bit (ignore 0-bits):

3. All intermediate calculation steps
- Position 7: bit = 1 → 1 × 2^7 = 1 × 128 = 128
- Position 6: bit = 1 → 1 × 2^6 = 1 × 64  = 64
- Position 5: bit = 1 → 1 × 2^5 = 1 × 32  = 32
- Position 4: bit = 0 → 0 × 2^4 = 0
- Position 3: bit = 0 → 0 × 2^3 = 0
- Position 2: bit = 1 → 1 × 2^2 = 1 × 4   = 4
- Position 1: bit = 1 → 1 × 2^1 = 1 × 2   = 2
- Position 0: bit = 0 → 0 × 2^0 = 0

Now sum: 128 + 64 + 32 + 0 + 0 + 4 + 2 + 0
128 + 64 = 192
192 + 32 = 224
224 + 4 = 228
228 + 2 = 230

4. Why the correct answer is correct
Each 1-bit's power-of-two contribution has been correctly computed and summed. The total decimal value of the binary 11100110 is therefore 230.

5. Why other answers would be incorrect
Common mistakes include reversing bit order (treating leftmost as position 0), misindexing positions by one, or omitting a 1-bit contribution. Any such error changes the powers of two used and yields an incorrect sum.

6. Conclusion
The decimal (base-10) value of binary 11100110 is 230, which matches the provided answer.

Below is a regular binary number: 11100110 Please write it’s base 10 value (e.g 14, 28, 183) in the space provided.简答题

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