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Digital Electronics
X
A
CB
1
X
X
X
A
CB
CB
CB
(a)
X
A
1
X
X
X
A
(b)
1
1
A
X
X
A
(c)
1
X
X
1
1
X
A
1
X
A
(d)
1
1
1
X
X
A
X
X
A
(e)
1
X
X
CB
CB
CB
CB
CB
CB
CB
CB
CB
CB
CB
CB
CB
CB
CB
CB
X
A
1
X
X
X
A
(f)
1
CB
CB
CB
CB
1
Figure 11.30 Karnaugh maps (example 11.9).
J B = AAC + AAC
(11.16)
K B = 1
(11.17)
J C = AAB
(11.18)
K C = A + B
(11.19)
• The hardware implementation is shown in Fig. 11.31.
• In the case where the unused inputs are considered as ‘don’t cares’, the circuit excitation table is
modified to that shown in Table 11.13.
• Modified Karnaugh maps are shown in Fig. 11.32.
• The minimized Boolean expressions are derived from the Karnaugh maps of Figs 11.32(a) to (f).
• Minimized expressions for J A , K A , J B , K B , J C and K C respectively are as follows:
J A = BBC
(11.20)
K A = 1
(11.21)
J B = 1
(11.22)
K B = 1
(11.23)
J C = B
(11.24)
K C = A
(11.25)
• Figure 11.33 shows the hardware implementation.