quiz1ans - ERG2020A Digital Logic Systems(Fall 2007 Quiz#1...

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ERG2020A: Digital Logic & Systems (Fall 2007) Quiz #1 Suggested Solution 1. Convert the following (positive numbers) numbers from the given bases to the other three bases listed in the table: (18%) Ans: 220 . 625 10 = DC . A 16 = 11011100 . 101 2 = 334 . 5 8 220 ÷ 16 = 13 . . . 12 0 . 625 × 16 = 10 10110011 . 01 2 = B3 . 4 16 = 263 . 2 8 = 11 × 16 + 3 + 1 16 × 4 = 179 . 25 10 A 7 . 6 16 = 10100111 . 011 2 = 247 . 30 8 = 10 × 16 + 7 + 1 16 × 6 = 167 . 375 10 Decimal Binary Octal Hexadecimal 220.625 11011100.101 334.5 DC.A 179.25 10110011.02 263.2 B3.4 167.375 10100111.011 247.30 A7.6 2. A7 16 is an eight bit unsigned numbers. Convert this number into a 12-bit signed binary number using the following formats (6%) Ans: (a) A7 16 = 1010 0111 2 Sign & magnitude: 0000 1010 0111 (b) One’s complement: 0000 1010 0111 (c) Two’s complement: 0000 1010 0111 3. Represent -A7 . 6 16 as a 12 + 4 (fraction) bits binary number using the three formats in Q2. (6%) Ans: -A7.6 = -(A7.6) = -(0000 1010 0111 0110) Sign & mag.: 1000 1010 0111 0110 One’s complement: 1111 0101 1000 1001 Two’s complement: 1111 0101 1001 1010 4. Use binary arithmetic to compute “A - B” (6%), “A × B” (8%), and “A / B” (10%; accurate up to 2 digits after the binary point) for the following unsigned numbers:
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