Express the number (01110110); (a number in binary system or base 2. into base 1

Question

Express the number (01110110); (a number in binary system or base 2. into base 10 (decimal) Express the number (67)10 (a number in decimal system or b3se 10) into base 2 (binary). Execute the f d lowing operations with the binary numbers given and check your results by converting each of (he numbers to their decimal (base 10) equivalents 101011 + 111111 + 111011 + 010101 1111 Times 1010 Construct a truth table for each of the following Construct a truth table for each of the following Let p and q be the propositions q: we are going to make a cheaper computer; q: we are going to lose business. Translate the following into symbolic form. If we make a cheaper computer, then we will lose business. If we lose business, then we will make a cheaper computer. We will lose business if and only if we mice a cheaper computer. If we lose business, then we will not m :e a cheaper computer. It is not (he case that we will lose business if and only if we do not make a cheaper computer.. Let p. q and r be (he propositions p: you get an A on the final exam of a course, q: you do every homework assigned in the .course, r: you get an A in the course. Write the following propositions using p. q and r and logical connectives. . You get an A in (he course, but you do net do all homework assisted. You get an A on the final; you do all homework assigned and get an A in the course. To get an A in the course, it is necessary for you to get an A on the final examination. You get an A on the final, but you don't do every homework assigned; nevertheless, you get an A in the course. Getting an A on the final and doing all homework assisted is suScient for getting an A in the course. if You will get an A in the course if and only if you either do all homework assigned or you get an A on the final,

Explanation / Answer

1)

a)

01110110

20*0+21*1+22*1+23*0+24*1+25*1+26*1+27*0

1+2+4+0+16+32+64+0

(119)10

b)

(67)10

(1000011)2

c)

(10111110)2

d)

(10010110)2

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2)

a)

b)

c)

d)

e)

f)

g)

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3)

a)

b)

c)

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4)

a)

p->q

b)

q->p

c)

q<->p

d)

q->~p

e)

~(q->~p)

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5)

a)

p^q

b)

p^(q^r)

c)

p^(~q->r)

d)

(q^r)->p

e)

p<->(qvr)

p q p^q    ~(p^q) T T T F T F F T F T F T F F F T

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