Question

HW 9: N-bit Arithmetic For each of the <X, Y> pairs in the table below: a) Convert X and Y to binary b) Compute X+Y (the 8-bit sum) c) Compute Y (the 2's complement of Y) d) Compute X-Y = X+Y (the 8-bit difference) e) Indicate the signs of X, Y, X+Y, Y, and X-Y f) Convert X+Y, Y, and X-Y to hexadecimal g) Indicate condition flag (z, n, C, v) values for X+Y, X-Y h) As unsigned numbers are X+Y and X-Y accurate? i) As signed numbers are X+Y and X-Y accurate? Where <X, Y> = 1) <0x47, 0x6B>

Answer 1

X = Ox 47 I y = Ox 6B = (6B), X = (4+) 16 = (0100 onll) 4 = (68) 16 = Collo 1011), x + y = ? - 4= 0100 0111 ouo 10!! x+y = 10110010 x+y = (10110010), = (178) 10 7 - 9 comple ) en+ (y) 2's complement = 1's complement ! is complement (Y) = 10010100 [ Reverse bits of y] g's complement (y) = 10010100 + 1 = 10010101 ' g's complement (4) = 10010101 @ x-y= ? 1 x - y = x + (-4) Here Y ir negative so, we apply 2's complement for y to make it as y. . -Y = 2's complemently). = 1001010 || Now , x= o 100 onll → Here MSB is 1 co, result is -Y = 1001010 negative and Result in present *+-Y) = 1101 1100 in 2's complement. We appl 2's complement for result to get value

Result = -(a's complement (1101110017 E-((00100100),] @). X = (0100 011), Here MSB is o so, it is positive. Pf MIB=0 then it is positive - MSB El then it is negative. Note! 2 Y = (0110 1011), Here MSB is a so, it is positive 7 x + y = (10110010), Here we have done un signed addition, so, No need to have a sign bit here. If we have done any signed addition, then MSB is signbit Y = 10010101 " Here MSB ir 1. so, it is negative Here ise is ', so, it is negative " x+y = (10110010), (x-4)= - (00100100) = B 2 =(B2) 16 = - (24)16 ✓ = (100101011, = 9 5 = (95), 11011100 -> x-Y =