Question

What is the binary base 2 representation of the number 176?(1 point) Responses 01111010 01111010 10110000 10110000 10101010 10101010 01111101

Answer 1

To convert the decimal number 176 to its binary representation:

1. Start with the largest power of 2 that fits into 176.
2. 128 (which is \(2^7\)) fits into 176. Subtract 128 from 176, which gives you 48.
3. The next largest power of 2 is 32 (which is \(2^5\)). Subtract 32 from 48, which gives you 16.
4. The next largest power of 2 is 16 (which is \(2^4\)). Subtract 16 from 16, which gives you 0.
5. No further powers of 2 are needed, and so we stop here.

Now we assemble the binary representation. The powers of 2 used are \(2^7\), \(2^5\), and \(2^4\), which corresponds to bits 7, 5, and 4 being set to 1, while all other bits (from \(2^6\), \(2^3\), \(2^2\), \(2^1\), and \(2^0\)) will be 0.

This is represented as follows in binary:

- \(2^7 \rightarrow 1\)
- \(2^6 \rightarrow 0\)
- \(2^5 \rightarrow 1\)
- \(2^4 \rightarrow 1\)
- \(2^3 \rightarrow 0\)
- \(2^2 \rightarrow 0\)
- \(2^1 \rightarrow 0\)
- \(2^0 \rightarrow 0\)

Putting it all together, the binary representation of the decimal number 176 is:

**10110000**

From your provided options, the correct answer is: **10110000**.