TUGAS 5

full adder

Full Adder menjumlahkan dua bilangan yang telah dikonversikan menjadi bilangan-bilangan biner. Masing-masing bit pada posisi yang sama saling dijumlahkan. Full Adder sebagai penjumlah pada bit-bit selain yang terendah. Full Adder menjumlahkan dua bit input ditambah dengan nilai Carry-Out dari penjumlahan bit sebelumnya. Output dari Full Adder adalah hasil penjumlahan (Sum) dan bit kelebihannya (carry-out).
prinsip kerja full adder

Penjumahan full adder pada prinsipnya menggunakan dua buah half adder dan sebuah gerbang OR. Half adder pertama merupakan penjumlahan A dan B . Selanjutnya nilai SUM dari half adder pertama diproses pada half adder kedua dengan input satu lagi yaitu C. Nilai half adder kedua itulah yang menjadi SUM selanjutnya. Carry pada half adder pertama diproses pada gerbang OR dan akan menjadi carry dari rangkaian full adder.

tugas 4

Hukum Aljabar Boolean

1. Hukum Komutatif

(a) A + B = B + A

Tabel Kebenaran:

A	B	A + B	B + A
0	0	0	0
0	1	1	1
1	0	1	1
1	1	1	1

(b) A B = B A

Tabel Kebenaran:

A	B	AB	BA
0	0	0	0
0	1	0	0
1	0	0	0
1	1	1	1

2. Hukum Asosiatif

(a) (A + B) + C = A + (B + C)

Tabel Kebenaran:

A	B	C	A + B	B + C	(A+B)+C	A+(B+C)
0	0	0	0	0	0	0
0	0	1	0	1	1	1
0	1	0	1	1	1	1
0	1	1	1	1	1	1
1	0	0	1	0	1	1
1	0	1	1	1	1	1
1	1	0	1	1	1	1
1	1	1	1	1	1	1

(b) (A B) C = A (B C)

Tabel Kebenaran:

A	B	C	AB	BC	(AB)C	A(BC)
0	0	0	0	0	0	0
0	0	1	0	0	0	0
0	1	0	0	0	0	0
0	1	1	0	1	0	0
1	0	0	0	0	0	0
1	0	1	0	0	0	0
1	1	0	1	0	0	0
1	1	1	1	1	1	1

3. Hukum Distributif

(a) A (B + C) = A B + A C

Tabel Kebenaran:

A	B	C	B +C	AB	AC	A(B+C)	(AB)+(AC)
0	0	0	0	0	0	0	0
0	0	1	1	0	0	0	0
0	1	0	1	0	0	0	0
0	1	1	1	0	0	0	0
1	0	0	0	0	0	0	0
1	0	1	1	0	1	1	1
1	1	0	1	1	0	1	1
1	1	1	1	1	1	1	1

(b) A + (B C) = (A + B) (A + C)

Tabel Kebenaran:

A	B	C	BC	A+B	A+C	A+(BC)	(A+B)(A+C)
0	0	0	0	0	0	0	0
0	0	1	0	0	1	0	0
0	1	0	0	1	0	0	0
0	1	1	1	1	1	1	1
1	0	0	0	1	1	1	1
1	0	1	0	1	1	1	1
1	1	0	0	1	1	1	1
1	1	1	1	1	1	1	1

4. Hukum Identity

(a) A + A = A

Tabel Kebenaran:

A	A + A
0	0
0	0
1	1
1	1

(b) A A = A

Tabel Kebenaran:

A	A A
0	0
0	0
1	1
1	1

5.

(a) AB + A B’

Tabel Kebenaran:

A	B	B'	A B	A B'	AB+AB'
0	0	1	0	0	0
0	1	0	0	0	0
1	0	1	0	1	1
1	1	0	1	0	1

(b) (A+B)(A+B’)

Tabel Kebenaran:

A	B	B'	A+B	A+B'
0	0	1	0	1
0	1	0	1	0
1	0	1	1	1
1	1	0	1	1

6. Hukum Redudansi

(a) A + A B = A

Tabel Kebenaran:

A	B	A B	A + A B
0	0	0	0
0	1	0	1
1	0	0	1
1	1	1	1

(b) A (A + B) = A

Tabel Kebenaran:

A	B	A + B	A (A + B)
0	0	0	0
0	1	1	0
1	0	1	1
1	1	1	1

7

(a) 0 + A = A

Tabel Kebenaran:

A	0 + A
0	0
0	0
1	1
1	1

(b) 0 A = 0

Tabel Kebenaran:

A	0 A	0
0	0	0
0	0	0
1	0	0
1	0	0

8

(a) 1 + A = 1

Tabel Kebenaran:

A	1 + A	1
0	1	1
0	1	1
1	1	1
1	1	1

(b) 1 A = A

Tabel Kebenaran:

A	1 A
0	0
0	0
1	1
1	1

9

(a) A’ + A = 1

Tabel Kebenaran:

A	A'	A'	1
0	1	1	1
0	1	1	1
1	0	1	1
1	0	1	1

(b) A’ A=0

Tabel Kebenaran:

A	A'	A'A	0
0	1	0	0
0	1	0	0
1	0	0	0
1	0	0	0

10

(a) A + A’ B =A + B

Tabel Kebenaran:

A	B	A'	A' B	A+B	A+A' B
0	0	1	1	0	0
0	1	1	0	1	1
1	0	0	1	1	1
1	1	0	0	1	1

(b) A (A’ + B) = AB

Tabel Kebenaran:

A	B	A'	A'+B	A B	A(A'+B)
0	0	1	1	0	0
0	1	1	1	0	0
1	0	0	0	0	0
1	1	0	1	1	1

11. TheoremaDe Morgan's

(a) (A’+B’)= A’B’

Tabel Kebenaran:

A	B	A'	B'	A+B	(A+B)'	A' B'
0	0	1	1	0	1	1
0	1	1	0	1	0	0
1	0	0	1	1	0	0
1	1	0	0	1	0	0

(b) (A’B’) = A’ + B’

Tabel Kebenaran:

A	B	A'	B'	A B	(AB)'	A'+B'
0	0	1	1	0	1	1
0	1	1	0	0	1	1
1	0	0	1	0	1	1
1	1	0	0	1	0	0

Quiz Aljabar Boolean

1. Give the relationship that represents the dual of the Boolean property A + 1 = 1?
(Note: * = AND, + = OR and ' = NOT)
1. A * 1 = 1
2. A * 0 = 0
3. A + 0 = 0
4. A * A = A
5. A * 1 = 1

2. Give the best definition of a literal?
1. A Boolean variable
2. The complement of a Boolean variable
3. 1 or 2
4. A Boolean variable interpreted literally
5. The actual understanding of a Boolean variable

3. Simplify the Boolean expression (A+B+C)(D+E)' + (A+B+C)(D+E) and choose the best answer.
1. A + B + C
2. D + E
3. A'B'C'
4. D'E'
5. None of the above

4. Which of the following relationships represents the dual of the Boolean property x + x'y = x + y?
1. x'(x + y') = x'y'
2. x(x'y) = xy
3. x*x' + y = xy
4. x'(xy') = x'y'
5. x(x' + y) = xy

5. Given the function F(X,Y,Z) = XZ + Z(X'+ XY), the equivalent most simplified Boolean representation for F is:
1. Z + YZ
2. Z + XYZ
3. XZ
4. X + YZ
5. None of the above

6. Which of the following Boolean functions is algebraically complete?
1. F = xy
2. F = x + y
3. F = x'
4. F = xy + yz
5. F = x + y'

7. Simplification of the Boolean expression (A + B)'(C + D + E)' + (A + B)' yields which of the following results?
1. A + B
2. A'B'
3. C + D + E
4. C'D'E'
5. A'B'C'D'E'

8. Given that F = A'B'+ C'+ D'+ E', which of the following represent the only correct expression for F'?
1. F'= A+B+C+D+E
2. F'= ABCDE
3. F'= AB(C+D+E)
4. F'= AB+C'+D'+E'
5. F'= (A+B)CDE

9. An equivalent representation for the Boolean expression A' + 1 is
1. A
2. A'
3. 1
4. 0

10. Simplification of the Boolean expression AB + ABC + ABCD + ABCDE + ABCDEF yields which of the following results?
1. ABCDEF
2. AB
3. AB + CD + EF
4. A + B + C + D + E + F
5. A + B(C+D(E+F))