Page 75 - DCAP108_DIGITAL_CIRCUITS_AND_LOGIC_DESIGNS

Digital Circuits and Logic Design

Notes
Step 5. Squares 6, 7, 10, and 11 form a quad. This quad is looped (loop 6, 7, 10, 11). Note
that square 11 is used again, even though it was part of loop 11, 15.
Step 6. All 1s have already been looped.

Step 7. Each loop generates a term in the expression for X. Loop 4 is simply ABCD . Loop
11, 15 is ACD (the B variable is eliminated). Loop 6, 7, 10, 11 is BD (A and C are
eliminated).
Figure 4.20: The K-map

Consider the K map in Figure 4.21 (b). Once again we can assume that Step 1 has already
been performed.
Step 2. There are no isolated 1s.
Step 3. The 1 in square 3 is adjacent only to the 1 in square 7. Looping d pair (loop 3, 7)
produces the term ACD.
Step 4. There are no octets.

Step 5. There are two quads. Squares 5, 6, 7, and 8 form one quad. Looping this quad
produces the term AB . The second quad is made up of squares 6, 9, and 10.

70 LOVELY PROFESSIONAL UNIVERSITY