Convert the following pairs of decimal numbers to 5-bit 2's-complement numbers, then add them. State whether or not overflow occurs in each case. (a) 4 and 11 (b) 6 and 14 (c)-13 and 12 (d) -4 and 8 (e) -2 and -9 (f) -9 and -14
Accepted Solution
A:
Step-by-step explanation:(a) 4 and 11 binary equivalent of 4 in 5 bit = 00100 binary equivalent of 11 in 5 bit = 01011 decimal number 4 in 2's complement form = 11100 decimal number 11 in 2's complement form = 10101now, 1 1 1 0 0 + 1 01 0 1 1 1 000 1Since, we are doing addition on 5 bit numbers but the result of addition came in 6 digit, so there will be overflow.(b) 6 and 14 binary equivalent of 6 in 5 bit = 00110 binary equivalent of 14 in 5 bit = 01110 decimal number 6 in 2's complement form = 11010 decimal number 14 in 2's complement form = 10010now, 1 1 0 1 0 + 1 00 1 0 1 0 1 1 0 0Since, we are doing addition on 5 bit numbers but the result of addition came in 6 digit, so there will be overflow. (c) -13 and 12 binary equivalent of -13 in 5 bit = 10011 binary equivalent of 12 in 5 bit = 01100 decimal number -13 in 2's complement form = 01101 decimal number 12 in 2's complement form = 10100now, 0 1 1 0 1 + 1 0 1 0 0 1 0 0 0 0 1Since, we are doing addition on 5 bit numbers but the result of addition came in 6 digit, so there will be overflow. (d) -4 and 8 binary equivalent of -4 in 5 bit = 11100 binary equivalent of 8 in 5 bit = 01000 decimal number -4 in 2's complement form = 00100 decimal number 8 in 2's complement form = 11000now, 0 0 1 0 0 + 1 1 0 0 0 1 1 1 0 0Since, we are doing addition on 5 bit numbers and the result of addition also came in 5 digit, so there will not be overflow.(e) -2 and -9 binary equivalent of -2 in 5 bit = 11110 binary equivalent of -9 in 5 bit = 10111 decimal number -2 in 2's complement form = 00010 decimal number -9 in 2's complement form = 01001now, 0 0 0 1 0 + 0 1 0 0 1 0 1 0 1 1Since, we are doing addition on 5 bit numbers and the result of addition also came in 5 digit, so there will not be overflow.(f) -9 and -14 binary equivalent of -9 in 5 bit = 10111 binary equivalent of -14 in 5 bit = 10010 decimal number -9 in 2's complement form = 01001 decimal number -10 in 2's complement form = 01110now, 0 1 0 0 1 + 0 1 1 1 1 1 1 000Since, we are doing addition on 5 bit numbers and the result of addition also came in 5 digit, so there will not be overflow.