200203 answers01
- 1. 1, convert the following binary numbers to decimal equivalents: A, 001100 B, 000011 C, 011100 D, 111100 E, 111111 Answer For the binary representation of ...}.{... 321012 −−−= bbbbbby , the value of Y is i i iby 2×= A, 001100 = 1248202021212020 012345 =+=×+×+×+×+×+× B, 000011 = 312212120202020 012345 =+=×+×+×+×+×+× C, 011100 = 284816202021212120 012345 =++=×+×+×+×+×+× D, 111100 = 6081632202021212121 012345 =++=×+×+×+×+×+× E, 111111 = 6312481632212121212121 012345 =+++++=×+×+×+×+×+× 2, Convert the following binary numbers to their decimal equivalents: A, 11100.001 B, 110011.10011 C, 101010101010.1 Answer For the binary representation of ...}.{... 321012 −−−= bbbbbby , the value of Y is i i iby 2×= A, 11100.001= 125.28125.0282120202020212121 32101234 =+=×+×+×+×+×+×+×+× −−− B, 110011.10011= 59375.5103125.00625.05.051 2121202021212120202121 54321012345 =+++= ×+×+×+×+×+×+×+×+×+×+× −−−−− C, 101010101010.1= 5.27305.028321285122048 21212121212121 11357911 =++++++= ×+×+×+×+×+×+× −
- 2. 3, Convert the following decimal numbers to their binary equivalents A, 64 B, 128 C, 256 D, 100 E, 111 F, 145 G, 255 Answer A, Quotient Remainder 64/2 32 0 32/2 16 0 16/2 8 0 8/2 4 0 4/2 2 0 2/2 1 0 1/2 0 1 210 100000064 = B, 210 10000000128 = C, 210 100000000256 = D, Quotient Remainder 100/2 50 0 50/2 25 0 25/2 12 1 12/2 6 0 6/2 3 0 3/2 1 1 1/2 0 1 210 1100100100 = E, Quotient Remainder 111/2 55 1 55/2 27 1 27/2 13 1 13/2 6 1 6/2 3 0 3/2 1 1 1/2 0 1 210 1101111111 = F, 210 1001000145 =
- 3. G, 255 Quotient Remainder 255/2 127 1 127/2 63 1 63/2 31 1 31/2 15 1 15/2 7 1 7/2 3 1 3/2 1 1 1/2 0 1 210 11111111255 = 4, Convert the following decimal numbers to their binary equivalents A, 34.75 B, 25.25 C, 27.1875 A, 34.75 the integer part (34) convert to binary format Quotient Remainder 34/2 17 0 17/2 8 1 8/2 4 0 4/2 2 0 2/2 1 0 1/2 0 1 210 10001034 = the fraction part (0.75) covert to binary format product integer part 0.75x2 1.5 1 0.5x2 1.0 1 210 11.075.0 = 210 11.10001075.34 = B, 25.25 the integer part is 25, convert to binary format Quotient Remainder 25/2 12 1 12/2 6 0 6/2 3 0 3/2 1 1 1/2 0 1 210 1100125 = the fraction part is 0.25, convert to binary format product integer part 0.25x2 0.5 0 0.5x2 1.0 1 => 0.01 210 01.025.0 = 210 01.1100125.25 =
- 4. C, 27.1875 the integer part is 27, convert to binary format Quotient Remainder 27/2 13 1 13/2 6 1 6/2 3 0 3/2 1 1 1/2 0 1 210 1101127 = the fraction part is 0.1875, convert to binary format product integer part 0.1875x2 0.375 0 0.375x2 0.75 0 0.75x2 1.5 1 0.5x2 1.0 1 210 0011.01875.0 = 210 0011.110111875.27 = 5, Convert the following hexadecimal number to their decimal equivalents a, C b, 9F c, B52 d, F117 e, ABCD f, 1111.1 g, 888.8 h, EBA.C Answer For the hexadecimal representation of ...}.{... 321012 −−−= xxxxxxy , the value of Y is i i ixy 16×= a, C = 121612 0 =× b, 9F= 1591615169 01 =×+× c, B52 = 28981621651611 012 =×+×+× d, F117 = 617191671611611615 0123 =×+×+×+× e, ABCD = 439811613161216111610 0123 =×+×+×+× f, 1111.1 = 0625.4369161161161161161 10123 =×+×+×+×+× − g, 888.8 = 5.2184168168168168 1012 =×+×+×+× − h, EBA.C 75.37701612161016111614 1012 =×+×+×+× −
- 5. 6, Convert the following decimal numbers to their hexadecimal equivalents a, 80 Quotient Remainder 80/16 5 0 5/16 0 5 1610 5080 = b, 2560 Quotient Remainder 2560/16 160 0 160/16 10 0 10/16 0 10 1610 002560 A= c, 65536 Quotient Remainder 65536/16 4096 0 4096/16 256 0 256/16 16 0 16/16 1 0 1/16 0 1 1610 1000065536 = d, 204.125 the integer part 204, convert to hexadecimal format Quotient Remainder 204/16 12 12 12/16 0 12 1610204 CC= the fraction part 0.125, convert to hexadecimal format product integer part 0.125x16 2.0 2 1610 2.0125.0 = 1610 2.125.204 CC=
- 6. e, 631.25 the integer part 631, convert to hexadecimal format Quotient Remainder 631/16 39 7 39/16 2 7 2/16 0 2 1610 277631 = the fraction part 0.25, convert to hexadecimal format product integer part 0.25x16 4.0 4 1610 4.025.0 = 1610 4.27725.531 = f, 100000.00390625 the integer part 100000, convert to hexadecimal format Quotient Remainder 100000/16 6250 0 6250/16 390 10 390/16 24 6 24/16 1 8 1/16 0 1 1610 0186100000 A= the fraction part is 0.00390625, convert to hexadecimal format product integer part 0.00390625x16 0.0625 0 0.0625x16 1.0 1 1610 01.000390625.0 = 1610 01.018600390625.100000 A=