Activity 2 How is the word length of a two’s complement representation changed without affecting its value? In this activity, we are going to study how the word length of a two’s complement representation is changed without affecting its value.

Activity 2 How is the word length of a two’s complement representation changed without affecting its value? Procedures 1.　Find out the 8-bit representation of two’s complement 　　of –410. 　　8-bit binary representation of 410 = 0000 01002 　　One’s complement of –410 　　　= 1111 2 　　Two’s complement of –410 　　　= 2 1011 1111 1100

Activity 2 How is the word length of a two’s complement representation changed without affecting its value? Procedures 2.　Find out the 16-bit representation of two’s complement 　　of –410. 　　16-bit binary representation of 410 = 2 　　One’s complement of –410 　　　 = 2 　　Two’s complement of –410 　　　 = 2 0000 0000 0000 0100 1111 1111 1111 1011 1111 1111 1111 1100

Activity 2 How is the word length of a two’s complement representation changed without affecting its value? Procedures 3.　Hence or otherwise, suggest the steps of converting a 　　two’s complement representation from m-bit to n-bit 　　(where n > m). 　　＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿ ＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿ ＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿ ＿＿＿＿＿＿＿＿＿＿＿＿ If the m-bit representation is non-negative (i.e the leftmost bit is 0), add or remove the leading ‘0’ to the left of the m-bit representation, forming an n-bit representation. If the m-bit representation is negative (i.e. the leftmost bit is 1), add or remove the leading ‘1’ to the left of the m-bit representation, forming an n-bit representation.

Activity 2 How is the word length of a two’s complement representation changed without affecting its value? Procedures 3.　Hence or otherwise, suggest the steps of converting a 　　two’s complement representation from m-bit to n-bit 　　(where n > m). 　　＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿ ＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿ ＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿ ＿＿＿＿＿＿＿＿＿＿＿＿ If the m-bit representation is non-negative (i.e the leftmost bit is 0), add or remove the leading ‘0’ to the left of the m-bit representation, forming an n-bit representation. If the m-bit representation is negative (i.e. the leftmost bit is 1), add or remove the leading ‘1’ to the left of the m-bit representation, forming an n-bit representation.