In signed 4-bit binary, the first bit is used to represent the sign of the number, with 0 indicating a positive number and 1 indicating a negative number. The remaining 3 bits are used to represent the magnitude of the number. Since 1000 has a 1 as its first bit, it is interpreted as a negative number. In 4-bit binary, the maximum value that can be represented is 7, so when we subtract 8 from 7, we get -1. Therefore, 1000 in signed 4-bit binary equals -8.
To convert a positive number to negative in signed 4-bit binary, we first take the positive number and represent it in 4-bit binary. Then, we flip all the bits (0s become 1s and 1s become 0s) and add 1 to the result. So, 1000 becomes 0111 and adding 1 to it gives us 1000, which is equal to -8 in signed 4-bit binary.
No, signed 4-bit binary can only represent numbers up to 7. This is because the first bit is used to represent the sign, leaving only 3 bits to represent the magnitude of the number. With 3 bits, we can represent a maximum value of 7 (111 in binary).
Signed 4-bit binary is commonly used in computer systems to represent integers in a compact and efficient way. It allows for a wider range of numbers to be represented using fewer bits compared to unsigned binary, which can only represent positive numbers.
Signed 4-bit binary is used in cases where we need to represent both positive and negative numbers in a compact format. This is common in computer systems where memory and storage space is limited. Signed 4-bit binary allows for a wider range of numbers to be represented using fewer bits, making it more efficient than unsigned binary in these cases.