Below is an unsigned ('regular') binary number:

00110111

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

Question

Below is an unsigned ('regular') binary number:

00110111

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

BlackTom AI · Accepted Answer

Convert the binary 00110111 to decimal by summing the values of the 1-bits at each binary place value.

1. Relevant knowledge points and concepts
- Binary is base-2: each bit represents a power of two.  
- For an 8-bit unsigned number, bits (from rightmost to leftmost) correspond to 2^0, 2^1, 2^2, ..., 2^7.  
- Leading zeros do not change the value. Grouping into nibbles can help: 0011 0111 = 0x37 in hexadecimal.

2. Step-by-step reasoning process
Write the bits with their place values (leftmost is bit 7):
- bit7 = 0 → 0 × 2^7
- bit6 = 0 → 0 × 2^6
- bit5 = 1 → 1 × 2^5
- bit4 = 1 → 1 × 2^4
- bit3 = 0 → 0 × 2^3
- bit2 = 1 → 1 × 2^2
- bit1 = 1 → 1 × 2^1
- bit0 = 1 → 1 × 2^0

3. Intermediate calculations
- 0 × 2^7 = 0 × 128 = 0
- 0 × 2^6 = 0 × 64 = 0
- 1 × 2^5 = 1 × 32 = 32
- 1 × 2^4 = 1 × 16 = 16
- 0 × 2^3 = 0 × 8 = 0
- 1 × 2^2 = 1 × 4 = 4
- 1 × 2^1 = 1 × 2 = 2
- 1 × 2^0 = 1 × 1 = 1

Sum these contributions: 32 + 16 + 4 + 2 + 1 = 55.

4. Why the correct answer is correct
Each 1-bit contributes the exact power-of-two value shown above. Adding those contributions yields the unique decimal value of the unsigned binary number. No sign bit or two's-complement interpretation is used because the problem specifies an unsigned (regular) binary number.

5. Why other answers would be incorrect
Common mistakes: ignoring bit order (reading right-to-left incorrectly), omitting powers (e.g., forgetting 2^2), or misinterpreting as signed/two's-complement (which would change value only if treating highest bit as sign). None of those apply here; the correct unsigned conversion is 55.

6. Conclusion confirming final answer
The unsigned binary 00110111 equals 55 in base 10, matching the provided answer.

Below is an unsigned ('regular') binary number: 00110111 Please write it’s base 10 value (e.g 14, 28, 183) in the space provided.Short answer

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