In Figure 8.8 we decomposed the function f by first identifying sub functions in the rows of the Karnaugh map. Repeat this decomposition by first identifying sub functions in the columns of the Karnaugh map.

x1x X3 X4 00 01 11 10 00 01 11 10 1 1 XI x2 X5 X4 1 1 1 1 X5 = 0 1 g X3 X4 k x1x 00 01 11 10 00 01 11 10 1 (a) Karnaugh map for the function f 1 1 X5 = 1 (b) Circuit obtained using decomposition 1