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}