Week 9(15) Written Homework.pdf - MAT 243 Week 9/15...

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MAT 243 Week 9/15 Written Homework 1. (a) (1 point) Convert the hexadecimal number FA to decimal and show your work. (b) (1 point) Convert the decimal number 1001 to octal and show your work. (c) (1 point) Carry out the hexadecimal addition CA10 + 4F57 directly in hexadecimal. Show your work. Do not convert the numbers to decimal, add them in decimal and convert the sum back to hexadec- imal. (d) (1 point) Carry out the binary multiplication 11011 times 1001 using only left bit shifts and addition. Show your work. 2. (a) (1 point) Explain how you multiply an octal number n directly in octal by (10) 8 . Illustrate your general explanation with n = (741) 8 . (b) (1 point) Explain how you divide an octal number directly in octal by (10) 8 . Here, divide means to carry out the division algorithm and to find both quotient and remainder. Illustrate your general expla- nation with n = (741) 8 . 3. (3 points) Given an integer n , show that you can multiply n by 35 using only five multiplications by 2, two additions and storing intermediate re- sults in memory.

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