7) Show how -65_(10) is represented in the following notations: a) Two's complement notation (2 Marks) b) Signed magnitude notation (2 Marks) c) Excess notation (2 Marks)

a) Two's complement notation:<br />To represent $-65_{10}$ in two's complement notation, we first find the binary representation of the positive number $65_{10}$. The binary representation of $65_{10}$ is $1000001_2$. To find the two's complement representation, we invert all the bits (change 0s to 1s and 1s to 0s) and then add 1 to the result. Inverting the bits of $1000001_2$ gives $1111110_2$. Adding 1 to this result gives $1111111_2$. Therefore, the two's complement representation of $-65_{10}$ is $1111111_2$.<br /><br />b) Signed magnitude notation:<br />In signed magnitude notation, the leftmost bit represents the sign of the number. A 0 represents a positive number, and a 1 represents a negative number. The remaining bits represent the magnitude of the number. For $-65_{10}$, the sign is negative, so the leftmost bit is 1. The magnitude is $65_{10}$, which is $1000001_2$ in binary. Therefore, the signed magnitude representation of $-65_{10}$ is $1 1000001_2$.<br /><br />c) Excess notation:<br />Excess notation is similar to two's complement notation, but the excess value is added to the magnitude to represent the signed number. The excess value is a fixed number that is added to the magnitude to get the signed number. For $-65_{10}$, we can use the same binary representation as in two's complement notation, which is $1111111_2$. The excess value for this representation is 1. Therefore, the excess notation representation of $-65_{10}$ is $1111111_2$.