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ece 251 hw 4 solutions, Exercises of Digital Electronics

solutions of jacob savirs homework 4 of digital design ece 251

Typology: Exercises

2018/2019

Uploaded on 09/26/2019

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NEW JERSEY INSTITUTE OF TECHNOLOGY
DEPT. OF ELECTRICAL & COMPUTER ENGINEERING
ACADEMIC YEAR 2011-2012
SEMESTER 1
EE251 Digital DESIGN
Solution HW4
1. The K-map:
Figure 1: K-map for Pb. 1
The simplified function:
2. Map of the original function:
Figure 2: K-map of the given function
K-Map of the simplified function:
Figure 3: Minimal cover
Therefore: .
3. The K-map:
Figure 4: Minimal cover for Pb. 3
Therefore, .
4. The K-map:
Figure 5: One possible minimal cover for Pb. 4.
Therefore: .
5. The function we need to implement is:
The K-map:
Figure 6: Minimal cover of G
Thus, . The NAND implementation:
Figure 7: NAND implementation
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NEW JERSEY INSTITUTE OF TECHNOLOGY

DEPT. OF ELECTRICAL & COMPUTER ENGINEERING

ACADEMIC YEAR 2011-

SEMESTER 1

EE251 Digital DESIGN

Solution HW

  1. The K-map:

Figure 1: K-map for Pb. 1 The simplified function:

  1. Map of the original function:

Figure 2: K-map of the given function K-Map of the simplified function:

Figure 3: Minimal cover Therefore:.

  1. The K-map:

Figure 4: Minimal cover for Pb. 3 Therefore,.

  1. The K-map:

Figure 5: One possible minimal cover for Pb. 4. Therefore:.

  1. The function we need to implement is:

The K-map:

Figure 6: Minimal cover of G Thus,. The NAND implementation:

Figure 7: NAND implementation

  1. We have:

The NOR implementation:

Figure 8: NOR implementation

  1. SOP form:

Figure 9: K-map for SOP (6 literals) POS form:

Figure 10: K-map for POS (7 literals) In this case, therefore, the SOP form is more economical.

  1. Based on the problem description, the output function of the circuit is

The K-map for this case:

Figure 11: K-map for Pb. 8 The function:. One possibility for circuit implementation:

Figure 12: Circuit for Pb. 8

  1. The truth table:

n xyz ABC 0 000 001 1 001 010 2 010 011 3 011 100 4 100 011 5 101 100 6 110 101 7 111 110

Circuit implementation:

Figure 17: Circuit for Pb. 10