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hw1_soln - Homework 1 Solutions ECE 0132 1 Problem 1...

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Homework 1 Solutions ECE 0132 September 29, 2005 1 Problem 1 Hexadecimal Decimal Octal Binary FADE 64222 175336 1111 1010 1101 1110 7D5 2005 3725 111 1101 0101 405 1029 2005 100 0000 0101 132 306 462 1 0011 0010 1.1 ( FADE ) 16 ( FADE ) 16 = 15 * 16 3 + 10 * 16 2 + 13 * 16 1 + 14 * 16 0 = (64222) 10 (1) = (1111 1010 1101 1110) 2 (2) = (175336) 8 (3) 1.2 (2005) 10 Quotient Remainder 2005 1002 1 501 0 250 1 125 0 62 1 31 0 15 1 7 1 3 1 1 1 0 1 (2005) 10 = (111 1101 0101) 2 (4) = (3725) 8 (5) = (7 D 5) 16 (6) 1
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1.3 (2005) 8 (2005) 8 = 2 * 8 3 + 0 * 8 2 + 0 * 8 1 + 5 * 8 0 = (1029) 10 (7) = (100 0000 0101) 2 (8) = (405) 16 (9) 1.4 (100110010) 2 (100110010) 2 = (462) 8 (10) = (132) 16 (11) = 1 * 16 2 + 3 * 16 1 + 2 * 16 0 = 306 (12) 2 Problem 2 2.1 (a) (2 D 0 . 9 F ) 16 = 2 * 16 2 + 13 * 16 1 + 0 * 16 0 + 9 * 16 - 1 + 15 * 16 - 2 (13) (720 . 6211) 10 (14) 2.2 (b) (364 . 1) 10 = (??) 8 (15) Integer part (divide by 8): Quotient Remainder 364 45 4 5 5 0 5 so, (364) 10 = (554) 8 (16) Fractional part (Multiply the fraction by 8 and keep the integer part of the result): 2
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Product Integer Part .1 .8 0 6.4 6 3.2 3 1.6 1 4.8 4 6.4 6 3.2 3 1.6 1 4.8 4 6.4 6 3.2 3 1.6 1 ...etc. then, ( . 1) 10 = ( . 06314631463146314 ... ) 8 (17) Therefore, (364 . 1) 10 = (554 . 06314631463146314 ... ) 8 (18) 2.3 (c) (100 110 101 . 011 1) 2 = (465 . 34) 8 (19) 2.4 (d) (3 . 1415) 8 = 3 * 8 0 + 1 * 8 - 1 + 4 * 8 - 2 + 1 * 8 - 3 + 5 * 8 - 4 (20) (3 . 1907) 10 (21) 3 Problem 3 3.1 (a) Hexadecimal: 1 1 3 A B 5 + 8 0 F E B B B 3 3
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3.2 (b) Binary: 1 1 0 0 1 1 × 1 0 1 0 1 0 1 1 0 0 1 1 1 1 0 0 1 1 + 1 1 0 0 1 1 1 0 0 0 0 1 0 1 1 1 1 0 3.3 (c) Octal: 1 6 5 . 2 1 + 3 2 . 0 1 1 1 7 . 2 2 4 Problem 4 4.1 (a) In decimal,
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