Download 5 Questions on Digital Design Circuits with Solution - Homework 1 | and more Study notes Microelectronic Circuits in PDF only on Docsity!
NEW JERSEY INSTITUTE OF TECHNOLOGY DEPT. OF ELECTRICAL & COMPUTER ENGINEERING ACADEMIC YEAR 2008- SEMESTER 1 ECE251 DIGITAL DESIGN SOLUTION HW
1. (4310) 6 = 4 6 3 + 3 6 2 + 1 6 1 = 864 + 108 + 6 = (^97810) (198) 13 = 1 13 2
- 9 13 1
- 8 = 169 + 117 + 8 = (^29410) 2. (a) (65) 10 = (1000001) 2 = (101) 8 = (41) 16 Long division by 2 Long division by 8 Long division by 16 Note: remainder column read upward. (b) (893) 10 = (1101111101) 2 = (1575) 8 = (37D) 16 Long division by 2 Long division by 8 Long division by 16 65 1 32 0 16 0 8 0 4 0 2 0 1 1 0 65 1 8 0 1 1 0 65 1 4 4 0
3. 1610 to 32 10 in base-5:= 31, 32, 33, 34, 40,…, 44, 100,… 111, 112 4. We first convert the two equations from octal to base 10 by converting all the coefficients. Since (35) 8 = (29) 10 , the new equations are: 2 2 3 29 x y x y The solution of this set of equations is: x = 7, y = 5 in base 10. Since 7 and 5 are also their representation in octal, the solution to these equations are x = (7) 8 , y = (5) 8. 5. (a) 3D 16 = 0011 1101 2 = 11 1101 2 000 111 101 = (^758) 3 16 + 13 = 48 + 13 = (^6110) 893 1 446 0 223 1 111 1 55 1 27 1 13 1 6 0 3 1 1 1 0 893 5 111 7 13 5 1 1 0 893 D 55 7 3 3 0 0 7 5
