FULL ADDER
Full adder adalah penjumlahan penuh dimana 3 buah input ( A B C )atau lebih dengan 2 buah output, dimana Sum ( S ) dan Carry ( Cn ). Full adder biasanya dapat menjumlahkan banyak bilangan biner dimana 8, 16, 32, dan jumlah bit biner lainnya. Pada Sum digunakan gerbang logika Ex-OR dan pada carry digunakan gerbang logika AND dan menggunakan gerbang logika OR untuk menjumlahkan tiap-tiap carry.
5A. Tabel Kebanaran
C
B
A
S
C
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
1
0
1
1
0
0
1
0
1
0
1
0
1
1
1
0
0
1
1
1
1
1
1
5B. Gambar Rangkaian
Dari tabel dapat disimpulkan bahwa percobaan yang Dilakukan adalah benar, karena hasil keluaran Sum dan Carry telah sesuai teori. Untuk output Sum, akan bernilai 0 jika salah satu atau ketiga-tiganya dari input bernilai 0, dan akan bernilai 1 jika salah sati atau ketiga-tiganya dari input bernilai 1. Sedangkan untuk output Carry, akan bernilai 0 jika ketiga-tiganya dari input bernilai 0 atau jika salah satu input bernilai 1, dan akan bernilai 1 jika ketiga-tiganya dari input bernilai 1 atau salah satu dari input bernilai 0.
Tugas 4.A
Hukum Aljabar Boolean & Tabel Kebenarannya
T1. Hukum Komutatif
(a) A + B = B + A
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
A
B
A B
B A
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)
A
B
C
A+B
(A+B)+C
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
1
1
1
1
1
1
1
1
1
1
1
1
(b) (A B) C = A (B C)
A
B
C
A B
(A B) C
B C
A (B C)
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
0
1
0
1
0
1
0
0
0
0
1
1
1
1
1
1
1
T3. Hukum Distributif
(a) A (B + C) = A B + A
A
B
C
B+C
A(B+C)
A B
AB+A
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
0
0
1
0
1
1
1
0
1
1
1
1
1
1
1
1
(b) A + (B C) = (A + B) (A + C)
A
B
C
B C
A+(BC)
A+B
A+C
(A+B)(A+C)
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
T4. Hukum Identity
(a) A + A = A
A A = A
T5.
(a) AB + AB’ = A
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
(A+B) (A+B’) = A
A
B
B’
A+B
A+B’
(A+B)(A+B’)
0
0
1
0
1
0
0
1
0
1
0
0
1
0
1
1
1
1
1
1
0
1
1
1
T6. Hukum Redudansi
(a) A + A B = A
A
B
A B
A+AB
0
0
0
0
0
1
0
0
1
0
0
1
1
1
1
1
(b) A (A + B) = A
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
(b) 0 A = 0
T8.
(a) 1 + A = 1
(b) 1 A = A
T9.
(a) A’ + A = 1
(b) A’ A = 0
T10.
(a) A + A’ B = A + B
A
B
A’
A’ B
A+A’B
A+B
0
0
1
0
0
0
0
1
1
1
1
1
1
0
0
0
1
1
1
1
0
0
1
1
(b) A ( A’ + B) = A B
A
B
‘ A’
A’+B
A(A’+B)
AB
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. Theorema De Morgan's
(a) ( A + B)’ = A’ B’
A
B
A’
B’
(A+B)’
A’B’
0
0
1
1
1
1
0
1
1
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
(b) ( A B )’ = A’ + B’
A
B
A’
B’
(A B)’
A’+B’
0
0
1
1
1
1
0
1
1
0
1
1
1
0
0
1
1
1
1
1
0
0
0
0
Tugas 4.B
1. Give the relationship that represents the dual of the Boolean property A + 1 = 1?
1. A * 1 = 1
2. A * 0 = 0 ( Jawabannya )
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 ( Jawabannya )
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 ( Jawabannya )
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' ( Jawabannya )
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 ( Jawabannya )
3. XZ
4. X + YZ
5. None of the above
6. Which of the following Boolean functions is algebraically complete?
1. F = xy ( Jawabannya )
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' ( Jawabannya )
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 ( Jawabannya )
9. An equivalent representation for the Boolean expression A' + 1 is
1. A
2. A'
3. 1 ( Jawabannya )
4. 0
10. Simplification of the Boolean expression AB + ABC + ABCD + ABCDE + ABCDEF yields which of the following results?
1. ABCDEF
2. AB ( Jawabannya )
3. AB + CD + EF
4. A + B + C + D + E + F
5. A + B(C+D(E+F))
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