Sample
EEE 21 Lecture
Variable Entered Mapping
Anastacia P. Ballesil
EEE Department, UP Diliman, QC
Example
Given:
F(A,B,C) = ∑m(0,1,4,7) G(A,B,C) =∑m(0,4,5)
F(A,B,C) + G(A,B,C) = ∑m(0,1,4,5,7) F(A,B,C) ⋅ G(A,B,C) = ∑m(0,4)
Anastacia P. Ballesil
EEE Department, UP Diliman, QC
F(A,B,C) AB C 0 1 00 1 1 01 0 0 11 0 1 10 1 0 AB C 0 1 00 1 0
G(A,B,C) 01 0 0 11 0 0 10 1 1
AB C 0 1
F+G 00 1 1 01 0 0 11 0 1 10 1 1 C
AB 0 1
F•G 00 1 0 01 0 0 11 0 0 10 1 0
Anastacia P. Ballesil
EEE Department, UP Diliman, QC
Example
Given:
F(A,B,C) = ∑m(0,1,4,7) H(A,B) = ∑m(0,2)
F(A,B,C) + H(A,B) = ? F(A,B,C) ⋅ H(A,B) = ?
Anastacia P. Ballesil
EEE Department, UP Diliman, QC
F(A,B,C) AB C 0 1 00 1 1 01 0 0 11 0 1 10 1 0 A B 0 1
H(A,B) = B’ 0 1 0 1 1 0
Can’t combine functions of different variables, or maps of different sizes
H(A,B,C) = B’ AB C 0 1 00 1 1 01 0 0 11 0 0 10 1 1
Anastacia P. Ballesil
EEE Department, UP Diliman, QC
CD EF 00 01 11 10 CD EF 00 01 11 10
00 1 1 0 0 00 1 0 0 1
(AB=00) 01 11 0 1 0 0 01 0 0 0 0 0 0 1 0 11 1 1 1 1
10 0 0 0 0 10 0 0 0 0
CD EF 00 01 11 10 CD EF 00 01 11 10
00 1 0 0 1 00 0 0 0 0
(AB=01) 01 11 0 1 0 0 01 0 0 0 0 0 0 1 0 11 0 0 1 0
10 0 0 0 0 10 0 0 0 0
(AB=10) Anastacia P. Ballesil
(AB=11) EEE Department, UP Diliman, QC
Variable Entered Mapping (VEM)
Adds another dimension to the simplification power of the K-map The list of map entries will be expanded to include not only {0,1,x} but also Boolean variables
Anastacia P. Ballesil
EEE Department, UP Diliman, QC
VEM Method
Convert the truth table to include Map-Entered Variables (MEV’s) as output Map the new outputs to corresponding cells in the K-map Read the resulting VEM
Anastacia P. Ballesil
EEE Department, UP Diliman, QC
VEM Method
Example: f(A,B,C) = ∑m(1,2,3,7)
ABC 000 001 010 011 100 101 110 111 f 0 1 1 1 0 0 0 1 AB f 00 01 10 11 {0,1,x, MEV}
Possible values: {0,1,x}
Variable Entered Mapping
Anastacia P. Ballesil
EEE Department, UP Diliman, QC
Example
Given:
F(A,B,C) = ∑m(0,1,4,7) G(A,B,C) =∑m(0,4,5)
F(A,B,C) + G(A,B,C) = ∑m(0,1,4,5,7) F(A,B,C) ⋅ G(A,B,C) = ∑m(0,4)
Anastacia P. Ballesil
EEE Department, UP Diliman, QC
F(A,B,C) AB C 0 1 00 1 1 01 0 0 11 0 1 10 1 0 AB C 0 1 00 1 0
G(A,B,C) 01 0 0 11 0 0 10 1 1
AB C 0 1
F+G 00 1 1 01 0 0 11 0 1 10 1 1 C
AB 0 1
F•G 00 1 0 01 0 0 11 0 0 10 1 0
Anastacia P. Ballesil
EEE Department, UP Diliman, QC
Example
Given:
F(A,B,C) = ∑m(0,1,4,7) H(A,B) = ∑m(0,2)
F(A,B,C) + H(A,B) = ? F(A,B,C) ⋅ H(A,B) = ?
Anastacia P. Ballesil
EEE Department, UP Diliman, QC
F(A,B,C) AB C 0 1 00 1 1 01 0 0 11 0 1 10 1 0 A B 0 1
H(A,B) = B’ 0 1 0 1 1 0
Can’t combine functions of different variables, or maps of different sizes
H(A,B,C) = B’ AB C 0 1 00 1 1 01 0 0 11 0 0 10 1 1
Anastacia P. Ballesil
EEE Department, UP Diliman, QC
CD EF 00 01 11 10 CD EF 00 01 11 10
00 1 1 0 0 00 1 0 0 1
(AB=00) 01 11 0 1 0 0 01 0 0 0 0 0 0 1 0 11 1 1 1 1
10 0 0 0 0 10 0 0 0 0
CD EF 00 01 11 10 CD EF 00 01 11 10
00 1 0 0 1 00 0 0 0 0
(AB=01) 01 11 0 1 0 0 01 0 0 0 0 0 0 1 0 11 0 0 1 0
10 0 0 0 0 10 0 0 0 0
(AB=10) Anastacia P. Ballesil
(AB=11) EEE Department, UP Diliman, QC
Variable Entered Mapping (VEM)
Adds another dimension to the simplification power of the K-map The list of map entries will be expanded to include not only {0,1,x} but also Boolean variables
Anastacia P. Ballesil
EEE Department, UP Diliman, QC
VEM Method
Convert the truth table to include Map-Entered Variables (MEV’s) as output Map the new outputs to corresponding cells in the K-map Read the resulting VEM
Anastacia P. Ballesil
EEE Department, UP Diliman, QC
VEM Method
Example: f(A,B,C) = ∑m(1,2,3,7)
ABC 000 001 010 011 100 101 110 111 f 0 1 1 1 0 0 0 1 AB f 00 01 10 11 {0,1,x, MEV}
Possible values: {0,1,x}