How can I tell a negative binary number from a positive one? More specifically, what exactly is the difference?

For example, the binary number 1110 converted to a decimal number results in either 14 (positive) or -2 (negative). So which one would I write as the correct answer? Or are both values correct?

(this is plagiarized) Adding a “1” to the front of it if the binary number is negative and a “0” if it is positive. However, using this sign-magnitude method can result in the possibility of two different bit patterns having the same binary value. For example, +0 and -0 would be 0000 and 1000 respectively as a signed 4-bit binary number.

in signed binary, both 0000 and 1000 are just 0

in ones-complement, 1000 = -7 since 0111 = 7
in twos-complement, 1000 = -8 since 0111 +1 = 1000 (or it may be treated as an error)

To determine whether a binary number is negative or positive, you need to understand how negative numbers are represented in binary.

In most computer systems, negative numbers are typically represented using a form of binary notation called "two's complement." In this representation, the most significant bit (MSB), which is the leftmost bit, is used to indicate the sign. If the MSB is 0, the number is positive, and if the MSB is 1, the number is negative.

In your example, the binary number 1110 has a 1 as the MSB, which means it is negative. To convert it to decimal, you would apply the conversion formula for two's complement:

- Flip all the bits (change 1s to 0s and vice versa): 1110 becomes 0001.
- Add 1 to the result: 0001 + 1 = 0010.

So in decimal form, 1110 represents -2, not 14. Therefore, -2 is the correct conversion for the binary number 1110.

In summary, to differentiate a negative binary number from a positive one:

1. Check the most significant bit (MSB).
2. If the MSB is 0, the number is positive.
3. If the MSB is 1, the number is negative in two's complement representation.

Remember to apply the appropriate conversion formula to obtain the decimal value when dealing with negative binary numbers.