2DISCRETE MATHEMATICS Question 5The maximum storage for a binary integer is 2 bytes is equivalent to 16bitswhich requires1,2,4,8,16,32,64,128,256,512,1024,2048,4096,8192,16384,32768 powers of 2 for its conversion. First we need to convert 21419∧24573into binary numbersAlgorithm for 21419214192Remainder1107092Remainder153542Remainder026772Remainder113382Remainder06692Remainder13342Remainder01672Remainder1832Remainder1412Remainder1202Remainder0102Remainder0
3DISCRETE MATHEMATICS 52Remainder122Remainder012Remainder102Remainder0 The process terminates upon reaching 0Hence 21419 into binary becomes 0101001110101011Repeating the same process for 24573 we get 0101111111111101Now adding 21419+24573 we get01010011101010110101111111111101 +1011001110101000Remember 1+1=10write0carry1And 1+1+1=11write1carry1Now convert 1011001110101000 back to decimal1011001110101000=1.215+0.214+1.213+1.212+0.211+0.210+1.29+1.28+1.27+0.26+1.25+0.24+1.23+0.22+0.21+0.20¿32768+0+8192+4096+0+0+512+256+128+0+32+0+8+0+0=45992(D)45992
4DISCRETE MATHEMATICS Question 6A company intends to send a letter to all its customers except males aged under 18. Suppose that age is an integer variable holding a customer's age, and gender is a character variable holding their sex (`M' for male and `F' for female). Which one of the following correctly expresses the condition that the customer is to be sent a letter?Let FrepresentsfemaleMrepresentsmaleF'representsfemale<18F''representsfemale≥18M'representsmale<18M''representsmale≥18The task is to find a set that does not contain ' , parties who are not supposed to receive letters(A)(age < 18) and (gender ='M').¿{F',M'}+{M',M''}={F',M',M''} the final set contains M'(B)(age < 18) and (gender ≠ 'M'). ¿{F',M'}+{F',F''}={F',M',F''} the final set contains M'(C)(age < 18) or (gender ='M').¿{F',M'}∨{M',M''}either of the sets contains M'(D)(age < 18) or (gender ≠'M'). ¿{F',M'}∨{F',F''}if the first set is preferred, M' will be inclusive and despite it still does not fully define for those who have to receive letters
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