X=00110,Y=11100 are represented in 5-bit signed 2's complement system. Then their sum X Y in 6-bit signed 2's complemented representation?? Please need explanation?

Question

Answer

Introduction:
In the signed 2's complement system, the leftmost bit represents the sign of the number. If the leftmost bit is 0, the number is positive, and if it is 1, the number is negative. In this system, the range of the numbers that can be represented is from -2^(n-1) to 2^(n-1)-1, where n is the number of bits used to represent the number.

Given:
X=00110, Y=11100 in 5-bit signed 2's complement system.

Conversion to decimal:
To convert the numbers to decimal, we need to check the sign bit. Since the leftmost bit of X is 0, X is positive, and its decimal value is 6. Since the leftmost bit of Y is 1, Y is negative, and its decimal value is -4.

Sum of X and Y:
To find the sum of X and Y, we add their decimal values. X+Y=6+(-4)=2.

Conversion to 6-bit signed 2's complement:
To represent the sum in 6-bit signed 2's complement, we need to check if it is positive or negative. Since the sum is positive, we represent it as a 6-bit binary number with the leftmost bit as 0. The binary representation of 2 is 000010 in 6-bit signed 2's complement.

Conclusion:
The sum of X and Y in 6-bit signed 2's complemented representation is 000010.

Answer

00010

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