Tugas 5

Tugas 5
Buatlah tabel penjumlah A= 5, B=3 dengan prinsip full adder, kemudian buat gambar rangkaian dan jelaskan prinsip kerjanya?

Rangkaian Full-Adder, pada prinsipnya bekerja seperti Half-Adder, tetapi mampu menampung bilangan Carry dari hasil penjumlahan sebelumnya.Rangkaian full adder dapat tersusun dari dua buah half adder. Di pasaran rangkaian full adder sudah ada yang berbentuk IC, seperti 74LS83 (4-bit full adder).

penjumlahan bilangan-bilangan biner hanya dengan penjumlahan bilangan desimal dimana hasil penjumlahan tersebut terbagi menjadi 2 bagian,yang SUMMARY(SUM) dan CARRY out(CARRY),apabila hasil penjumlahan pada suatu tingkat atau kolom melebihi nilai maksimumnya maka output CARRY akan berada pada keadaan logika 1.

Prinsip kerja:
Penjumahan full adder pada prinsipnya menggunakan dua buah half addaer 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 padagerbang OR.

Tabel Kebenaran

Tugas 4

Hukum Aljabar Boolean

T1. 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

T2. 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

T3. 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

T4. 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

T5.

(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

T6. 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

T7

(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

T8

(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

T9

(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

T10

(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

T11. 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))