document.write( "Question 1201883: How many 11-bit strings (that is, bit strings of length 11) are there which:
\n" ); document.write( "a)Start with the sub-string 011?
\n" ); document.write( "b)Have weight 6 (i.e., contain exactly 6 1’s) and start with the sub-string 011?
\n" ); document.write( "c)Either start with 011 or end with 01 (or both)?
\n" ); document.write( "d)Have weight 6 and either start with 011 or end with 01 (or both)? \n" ); document.write( "

Algebra.Com's Answer #836442 by ikleyn(52787) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "How many 11-bit strings (that is, bit strings of length 11) are there which:
\n" ); document.write( "a) Start with the sub-string 011?
\n" ); document.write( "b) Have weight 6 (i.e., contain exactly 6 1’s) and start with the sub-string 011?
\n" ); document.write( "c) Either start with 011 or end with 01 (or both)?
\n" ); document.write( "d) Have weight 6 and either start with 011 or end with 01 (or both)?
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\n" ); document.write( "\n" ); document.write( " Too many questions for one post.
\n" ); document.write( " I will answer first two to get you start.\r
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document.write( "(a)  In this part, you consider 11-bit strings (the string consisting of ones and zeroes).\r\n" );
document.write( "     that starts with substring 011.\r\n" );
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document.write( "     So, the remaining part of these strings is of the length 11-3 = 8.\r\n" );
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document.write( "     In these 8 positions, we may have 0 or 1 in each position, \r\n" );
document.write( "     independently of what is in other 7 remaining positions.\r\n" );
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document.write( "     The number of possibilities is   = 256.    ANSWER\r\n" );
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document.write( "(b)  In this part, you consider 11-bit strings, that have precisely 6 ones\r\n" );
document.write( "     and start with the substring 011.\r\n" );
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document.write( "     So, the remaining part of these strings is of the length 11-3 = 8 \r\n" );
document.write( "     and has precisely 6 ones.\r\n" );
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document.write( "     The number of ways to select 6 positions among 8 positios for these 6 ones\r\n" );
document.write( "     is   =  =  = 4*7 = 28.    ANSWER\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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\n" ); document.write( "\n" ); document.write( "Regarding two other parts (c) and (d), keep in mind that in my post
\n" ); document.write( "I gave you ALL NECESSARY ideas on how to complete the remaining parts.\r
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\n" ); document.write( "\n" ); document.write( "So, if you really want to learn the subject, you should apply this knowledge
\n" ); document.write( "and complete parts (c) and (d) ON YOUR OWN.\r
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