Digital Electronics: Principles, Devices and Applications

50 Digital ElectronicsCase 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 follows00100101+ 0001001000110111• 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+ 1110111000010011• 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+ 0001001011101101• The decimal equivalent of (11101101) 2 , which is in 2’s complement form, is −19, which is thecorrect answer. 2’s complement representation was discussed in detail in Chapter 1 on numbersystems.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: