Select one of the numbers we have used in base 2 and write the negative of that

Question

Select one of the numbers we have used in base 2 and write the negative of that number: Now add the negative of that number to the original number. Show the problem here with your answer. State the Distributive Property of Multiplication over Addition using A, B and C. Demonstrate the Distributive Property using 13five, 101five and 10five in any combination you choose. Then calculate each side and show that each side equals the same number (i.e. add first then multiply on one side and distribute first then add on the other).

Explanation / Answer

LET US CONSIDER

53 TO BASE 10

USING BASE 8 SYSTEM THIS IS 65

NOW CONVERTING TO BASE 2 ..WE GET

110101 ...IN BASE 2

MATHEMATICALLY WE CAN WRITE THIS AS

- 110101 ...AS USUAL ..THERE IS NOTHING WRONG IN IT

BUT IN COMPUTER TERMINOLOGY , IT IS WRITTEN IN A DIFFERENT MANNER ...

WHICH ONE DO YOU WANT ?

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DISTRIBUTIVE PROPERTY

WE SAY MULTIPLICATION DISTRIBUTES OVER ADDITION ...

THAT IS

A*[B+C] = A*B + A*C

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FIRST LET US FIND IN Z5 ....

WE HAVE IN Z5

13= 5*2+3=3[MOD 5]

101=5*20+1 = 1[MOD 5]

10= 5*2+0 = [0 MOD 5]

SO WE GET

13*[101+10] = 3[1+0] =3*[1] = 3

ALTERNATELY USING THE DISTRIBUTIVE PROPERTY

13*[101+10] = 3[1+0] =3*1+3*0 = 3+0 = 3

SO WE GET 3 TO Z 5 IN BOTH CASES

SO MULTIPLICATION DISTRIBUTES OVER ADDITION .

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