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EXERCICE 2 Convert to binary (2's complement) using a compact notation (minimum number of digits). Number in base 10 Number in base 2 (2's complement) +126.5 -25.8125 1.375 +10.37890625 13.62109375 15.61328125 2.99609375 EXERCICE 3 Give the result of the following set of additions in 8-bit 2's complement. Addends are also in 8-bit 2's complement. Indicate by YES or NO if an overflow occurs. Addition Result Overflow ? 0011 1000 0110 0000 1011 1000 1110 0000 1100 1000 1100 1000 1000 1000 1000 1000

Answer 1

+ 126.5 First we need to convert + 126.5 into binary no system to represent (+) sign we use �0� and in case of (-) we use �1� 2 126 2 63 0 2 31 1 2 14 1 2 15 1 2 7 1 2 3 1 1 1 Therefore 126 in binary = 111 111 0 and 0.5 times 2 = 1.0 Therefore we can write + 126.5 = 111 1110.1 (in binary) 2�s complement of (01111110.1) rightarrow 10000001.1 -25.8125 2 25 2 12 1 2 6 0 2 3 1 1 Therefore 25 in binary 11001 and 0.8125 times 2 = 1.625 1 0.625 times 1.25 1 0.25 times 2 = 0.50 0 0.5 times 2 = 1.0 1 Therefore we can write -25.8125 = 111001.1101 Therefore 2�s complement of (111001.1101): 000110.0011 -1.375 1 in binary = 1 and 0.375 times 2 = 0.75 0 0.75 times 2 = 1.5 1 0.5 times 2 = 1.0 1

For the first part first we need to find the binaar value of the given no and then convert that into his 2's complement from.

And for the second part simply we need to add the numbers and if no of bit>8

Then overflow occurr else not.And then convert the results into 8 bit 2's complement representation.