CSE 241 Lecture Notes - Lecture 8: Parity Bit, Karnaugh Map, George Boole

• School: University at Buffalo
• Department: Computer Science & Engineering
• Course: CSE 241
• Professor: Ramamurthy Bina

Document Summary

Last class: boolean algebraic simplification k-map plots minterms are plotted on a map. This map has 1 cell/minterm i. e. f(x,y) 2 variable map. 22 = 4 minterms: m0, m1, m2, m3 x\y y = 0 y = 1 x = 0. 3-variable k-map: 23 = 8 minterms w\xy xy=00 xy=01 xy=11 xy=10 w=0 m0 m1 w=1 m4 m5 m3 m7 m2 m6. 4-variable k-map: 24 = 16 minterms wx\yz yz=00 01 wx=00 m0 m4 m12 m8. F1(a, b, c) = (1, 4, 5, 6, 7) B ______ f1 (cid:894)a, b, c(cid:895) ______f(cid:894)(cid:895) is true for (1, 4, 5, 6, 7) Simplify this to minimum number of terms and minimum number of literals. Start: 5 terms -> 5x3 = 15 literals. Step 1: draw the empty k-map; label cells. Step 2: plot the (cid:1005)"s for the (cid:373)i(cid:374)ter(cid:373)s defi(cid:374)i(cid:374)g the fu(cid:374)(cid:272)tio(cid:374) *step 3: group the (cid:1005)"s i(cid:374)to largest rectangular group and cover all the (cid:1005)"s (cid:271)(cid:455) smallest number of groups.