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Unformatted text preview: Name Solution Digital Logic I EE 27202 Midterm Examination 1 3 October 2011, 14:4015:30 CDT Exam Rules Use only a pencil or pen. No calculators of any kind are allowed. Texting is out of the question. Alias Logic Won Problem 1 (15 pts) Problem 2 (9 pts) Problem 3 (9 pts) Problem 4 (24 pts) Problem 5 (9 pts) Problem 6 (9 pts) Problem 7 (16 pts) Problem 8 (9 pts) Exam Total (100 pts) Good Luck! Problem 1: (15 pts) Perform the conversions indicated below. For conversions to decimal all you need to show is the arithmetic that needs to be done to compute the value, theres no need to perform the computation. For example, a decimal value can be written as 12 + 3 4 5+6 + 7 9 . This only applies to answers in decimal. checked Convert 257 10 to hexadecimal. Hint: 16 2 = 256 . Hmmm . . . the value of a 4digit hexadecimal number consisting of digits d 2 d 1 d is d 2 16 2 + d 1 16 + d . Now, we need to find digits such that d 2 256 + d 1 16 + d = 257 10 . That must mean d 2 = 1 and d 1 = 0 and d = 1 . So the number in hex is 101 16 . checked Convert 2 f 7 16 to decimal. The value is 2 16 2 + 15 16 + 7 which is sufficient to get full credit. But for completeness, thats 759 10 in decimal. checked Convert 2 .f 7 16 to decimal. (Dont overlook the radix point.) The only difference here is the exponents on the 16s. The value is 2 16 + 15 16 1 + 7 16 2 . For com pleteness, thats 759 10 256 10 = 2 . 96484375 in decimal. checked Convert 257 9 to decimal. Here we use powers of 9. The value is 2 9 2 + 5 9 + 7 . For completeness, thats 214 10 in decimal. checked Convert 1011 0100 2 to decimal. Here we use powers of 2. The value is 2 7 + 2 5 + 2 4 + 2 2 , which is 180 10 . Note that terms for the digits of value zero were omitted, and the 1 was omitted from terms for the digits of value 1. Those with more experience might by eye convert it to b 4 16 then compute 11 16 + 4 = 180 . 2 Problem 2: (9 pts) Perform the conversions below, taking advantage of the fact that all radices are powers of 2. checked Convert abc 16 to binary. Because the radix is a power of 2, 16 = 2 4 , we know that each digit corresponds to, in this case, 4 bits. If the starting radix were 2 r each digit would correspond to r bits. So we convert each hex digit into 4 bits. Maybe we remember that a 16 = 1010 2 , if not its easy enough to derive. Given that we can convert the other two hex digits: b 16 = 1011 2 and c 16 = 1100 2 . Combining them gives the binary number 1010 1011 1100 2 . checked Convert abc 16 to octal. We can convert from binary to a radix that is a power of 2, say 2 s , by arranging the digits into groups of s and then converting each group to a digit. For octal (radix 8) we have s = 3 , so we need to group digits by 3s: 1010 1011 1100 2 = 101 010 111 100 2 = 5274 8 So the answer is 5274 8 ....
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