Write short notes on signed binary numbers and unsigned binary numbers
Signed binary numbers and unsigned binary numbers are two different representations of binary numbers.
1. Unsigned Binary Numbers:
- Unsigned binary numbers represent only positive numbers.
- In unsigned binary representation, the leftmost bit (most significant bit) represents the weight of 2 raised to the power of the number of bits in the binary number.
- The remaining bits represent smaller weights in decreasing order.
- For example, in an 8-bit unsigned binary number, the leftmost bit represents 2^7, the next bit represents 2^6, then 2^5 and so on until the rightmost bit represents 2^0.
- Unsigned binary numbers are useful when dealing with only positive values or when the range of values is known to be positive.
2. Signed Binary Numbers:
- Signed binary numbers represent both positive and negative numbers.
- In signed binary representation, the leftmost bit (most significant bit) is used to represent the sign of the number. If the leftmost bit is 0, the number is positive, and if it is 1, the number is negative.
- The remaining bits represent the magnitude of the number.
- The most common representation for negative numbers is the Two's Complement representation, where the magnitude of the negative number is obtained by finding the one's complement (flipping the bits) of its positive counterpart, then adding 1 to the result.
- The range of numbers that can be represented with signed binary numbers is usually symmetric, with an equal number of positive and negative values.
- Signed binary numbers are used in various applications where both positive and negative numbers need to be represented, such as in mathematical operations and in computer programming languages.