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Digital Electronics
Case 1
• Consider the decimal numbers +37 and +18.
• The 2’s complement of +37 in eight-bit representation = 00100101.
• The 2’s complement of +18 in eight-bit representation = 00010010.
• The addition of the two numbers, that is, +37 and +18, is performed as follows
00100101
+ 00010010
00110111
• The decimal equivalent of (00110111) 2 is (+55), which is the correct answer.
Case 2
• Consider the two decimal numbers +37 and -18.
• The 2’s complement representation of +37 in eight-bit representation = 00100101.
• The 2’s complement representation of −18 in eight-bit representation = 11101110.
• The addition of the two numbers, that is, +37 and −18, is performed as follows:
00100101
+ 11101110
00010011
• The final carry has been disregarded.
• The decimal equivalent of (00010011) 2 is +19, which is the correct answer.
Case 3
• Consider the two decimal numbers +18 and −37.
• −37 in 2’s complement form in eight−bit representation = 11011011.
• +18 in 2’s complement form in eight−bit representation = 00010010.
• The addition of the two numbers, that is, −37 and +18, is performed as follows:
11011011
+ 00010010
11101101
• The decimal equivalent of (11101101) 2 , which is in 2’s complement form, is −19, which is the
correct answer. 2’s complement representation was discussed in detail in Chapter 1 on number
systems.
Case 4
• Consider the two decimal numbers −18 and −37.
• −18 in 2’s complement form is 11101110.
• −37 in 2’s complement form is 11011011.
• The addition of the two numbers, that is, −37 and −18, is performed as follows: