ch 1Marcovitz_Ch1_Solutions_Fall2011

ch 1Marcovitz_Ch1_Solutions_Fall2011 - EC262 Digital...

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1 EC262 Digital Systems Fall 2011 Chapter 1 Solutions Textbook: Marcovitz, Introduction to Logic Design , 3 rd ed. Exercise 1 (b and c), Exercise 2 (b and c), Exercise 3 (b and d), Exercise 5 (b and c), Exercise 6 (d, f, g and h), Exercise 7 (a, b, e and f) and Exercise 10 (a, e and f). Exercise 1 : Convert unsigned binary integer to decimal. b. 1000000 = 2 6 = 64 c. 1001101101 = 2 0 + 2 2 + 2 3 + 2 5 + 2 6 + 2 9 = 1 + 4 + 8 + 32 + 64 + 512 = 621 Exercise 2 : Convert decimal to 12-bit unsigned binary. b. 127 Method 1: Result 127 127 - 2 6 = 63 63 - 2 5 = 31 31 – 2 4 = 15 15 – 2 3 = 7 7 – 2 2 = 3 3 – 2 1 = 1 2 7 > 127 2 6 63 2 5 31 2 4 15 2 3 7 2 2 3 2 1 1 2 0 _ _ _ _ _ 1 _ _ _ _ _ _ _ _ _ _ _ 1 1 _ _ _ _ _ _ _ _ _ _ 1 1 1 _ _ _ _ _ _ _ _ _ 1 1 1 1 _ _ _ _ _ _ _ _ 1 1 1 1 1 _ _ _ _ _ _ _ 1 1 1 1 1 1 _ _ _ _ _ _ 1 1 1 1 1 1 1 0 0 0 0 0 1 1 1 1 1 1 1 (12 bits) c. 402 Method 2: Result 402 / 2 = 201 201 / 2 = 100 100 / 2 = 50 50 / 2 = 25 25 / 2 = 12 12 / 2 = 6 6 / 2 = 3
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ch 1Marcovitz_Ch1_Solutions_Fall2011 - EC262 Digital...

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