SOLUTIONS - University of California, San Diego
[Pages:6]SOLUTIONS:
1. a. F (A,B,C) = A' B' C' + A' B' C + A B' C' + A B' C + A B C' + A B C [Distributive] = A'B' (C' + C) + AB' (C' + C) + AB (C' + C) [ Complementarity] = A'B' + AB' + AB [Idempotency] = A'B' + AB' + AB' +AB [ Distributive] = B' (A' + A) + A (B' + B) [ Complementarity] = B' + A
b. F(A,B) = (A'+B) ( A+B) [Distributive]
= AA' + A'B+ AB+ BB [Complementarity ]
= A'B+AB+BB [Distributive]
= B ( A'+A+1) [Complementarity]
= B . 1
[ identity ]
= B
2. a.
a'b' + a'c' + bc' [Complementarity & Distributive] = a'b' + (a'c'b'+a'c'b) + bc' [combining] = (a'b' + a'b'c') + (bc'a' + bc')[ commutativity & associativity] = a'b' + bc'[covering]
b. (a'+ b)(a'+ c')(b'+ c') [Associative] = (a'+ b)(b'+ c')(a'+ c')[commutativity] = (a'+ b)(b'+ c')[consensus]
3. a) Truth Table
b) SOP Y0 = (A'B'C'D)+(A'B'CD')+(A'BC'D')+(A'BCD)+(AB'C'D')+(AB'CD)+(ABC'D)+(A BCD') Y1= (A'B'CD)+(A'BC'D)+(A'BCD')+(A'BCD)+(AB'C'D)+(AB'CD')+(AB'CD)+(AB C'D')+(ABC'D)+(ABCD') Y2 = ABCD c) POS Y0= (A+B+C+D)(A+B+C'+D')(A+B'+C+D')(A+B'+C'+D)(A'+B+C+D')(A'+B+C'+ D)(A'+B'+C+D)(A'+B'+C'+D') Y1= (A+B+C+D)(A+B+C+D')(A+B+C'+D)(A+B'+C+D)(A'+B+C+D)(A'+B'+C'+D' ) Y2 = M (0,1,2,3,4,5,6,7,8,9,10,11,12,13,14)
4. a.
The simplified function is: F = B'D + A'B'C' + ACD + ABD' b.
5. a.
F(A,B,C,D) = (A + B' + C')(A + B + C)
b.
F(A,B,C,D) = D (A' + C') 6. a.
Since the universal gates {AND, OR, NOT can be constructed from the NAND gate, it is universal.
b. The given function is universal.
7. a.
Hence, the result is proved. The same result will be obtained for Expansion for y and Expansion for z (Try it!!!)
b.
Thus, proved. Same result will be obtained for Expansion for y. 8. f (a, b, c, d) = Sm(0,1, 2, 3, 4, 5, 7,8,12) + S d(10,11)
................
................
In order to avoid copyright disputes, this page is only a partial summary.
To fulfill the demand for quickly locating and searching documents.
It is intelligent file search solution for home and business.
Related download
- math camp 1 functional analysis
- homework 3 solutions c f a b c d m
- math 2000 assignment 9 solutions in logical
- written homework 6 solutions university of texas at austin
- solutions university of california san diego
- homework 7 home ucla mathematics
- solutions to assignment 3 ucb mathematics
- two fundamental theorems about the definite integral
- the riemann integral
- math 436 notes functions and inverses
Related searches
- university high school san diego ca
- university of california essay prompts
- university of california supplemental essays
- university of california free tuition
- university of california campuses
- university of california online certificates
- preliminary change of ownership san diego ca
- address university of california irvine
- university of california at irvine ca
- university of california irvine related people
- university of california irvine staff
- university of california irvine employment