Answer to Question #119557 in MathCAD for desmond

Question

.Using 8’s complement arithmetic compute the value of 6278-6758 and write your final answer in decimal

Answer 1

1) convert Decimal to Octal:

6278/8 = 784(Quotient) and 6(Remainder)

784/8 = 98(Quotient) and 0(Remainder)

98/8 = 12(Quotient) and 2(Remainder)

12/8 = 1(Quotient) and 4(Remainder)

1/8 = 0(Quotient) and 1(Remainder)

X = 6278₁₀ = 14206₈

Y = 6758₁₀ = 15146₈

2) find 8's complement of the Y (8's complement of a number is 1 added to it's 7's complement number):

77777₈ - 15146₈ = 62631₈

62631₈ + 1₈ = 62632₈

3) now Add this 8's complement of Y to X:

14206₈ + 62632₈ = 77040₈

4) here there is no carry, then answer is the 8's complement of the sum obtained with a minus:

77777₈ - 77040₈ = 737₈

737₈ + 1₈ = 740₈

result: -740₈

5) convert Octal to Decimal:

-740₈ = -(7*8²+4*8¹+0*8⁰) = -480₁₀

6) check:

6278 - 6758 = -480

Answer: -480