please answer question 6,7,8 and 9 from exer 1.4

30 Chapter 1 Fundamentals Since F is in position 5. its binary representation is (00101)2, and so on. Now choose an unrelated "dummy" message exactly five times as long (padded with a few extra letters if necessary). Place the dummy message in a third row. The letters of the dummy message correspond exactly to the string of O's and I's in the second row of the above table. We agree to write each letter in one font (say Times Roman) if it corresponds to a 0 in the table, and another font (say Times Roman Italic) if it corresponds to a 1 (Bacon used fonts that were even more similar). Thus if the dummy message is ONCE UPON A TIME IN THE WEST THERE WAS A TOWN, we would write that message as ONCE UPON A TIME IN THE WEST THERE WAS A TOWN. Note that when the letters in this message are arranged in a third row of the table, the patterns of nonitalic for 0 and italic for I allow us to decode the message. F L E E N w 00101 01011 00100 00100 01101 01110 10110 ONCEU PONAT MEIN THEWE STTHE REWAS ATOWN o Example 16 Suppose that we wish to decode the following dummy message, using the Bacon code NOW IS THE TIME FOR ALL GOOD MEN TO AID THE COUNTRY Since there are 40 letters, the true message must have 8 letters. Arrange the dummy message, 5 letters at a time in the following table, and then list the corresponding binary digits, using for italic and 0 for plain text. NOWIS THETI MEFOR ALLGO ODMEN TOAID THECO UNTRY 10010 1001100000 10001 10011 01001 01110 00001 The binary representations in the second row correspond respectively to the num- bers 18, 19,0,17,19,9,14 and 1, and therefore represent the letters STARTJOB Thus the decoded message is START JOB. If the fonts used are quite similar, it will not be obvious that the text is a coded message. Thus this example also illustrates steganography, the science of concealment of coded information. Modern versions include hiding information in stray bits of a digital photograph. One use of this is to watermark copyrighted artistic material. 1.4 Exercises In Exercises through 4. for the given integers m and n, write In Exercises 6 through 9, find the greatest common divisor mas on +r, with or