Question: 1a. (5) Simplify the Boolean expression F(x,y,z) = xyz + xyz +xyz using three-variable K-Maps show (a) the Truth Table, (b) the K-Map and (c)
1a. (5) Simplify the Boolean expression F(x,y,z) = xyz + xyz +xyz using three-variable K-Maps show (a) the Truth Table, (b) the K-Map and (c) simplified function.
b. Given the following Truth Table show (a) unsimplified MINTERM expression (b) form the K-Map and (c) simplified Boolean expression.
| Inputs | Output | |||
| A | B | C | D | Y |
| 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 1 |
| 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 1 | 1 | 1 |
| 0 | 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 1 | 1 |
| 0 | 1 | 1 | 0 | 1 |
| 0 | 1 | 1 | 1 | 1 |
| 1 | 0 | 0 | 0 | 0 |
| 1 | 0 | 0 | 1 | 1 |
| 1 | 0 | 1 | 0 | 0 |
| 1 | 0 | 1 | 1 | 1 |
| 1 | 1 | 0 | 0 | 0 |
| 1 | 1 | 0 | 1 | 1 |
| 1 | 1 | 1 | 0 | 0 |
| 1 | 1 | 1 | 1 | 1 |
c. Consider BCD (8421) which uses the binary numbers (0000 1001) and the six combinations (1010, 1011, 1100, 1101, 1110, and 1111) are not used by the BCD code. These combinations are called dont cares. These are shown as Xs on a K-Map and including the dont cares (Xs) in loops on a map can help to further simplify Boolean expressions. Simplify the Boolean expression d are the dont cares:
F = (0,1,3,5,9,12)+ d(2,4,6,7)
Using four-variable K-Maps show (a) the Truth Table, (b) the K-Map and (c) simplified function.
Above is 1a, b, c for my digital circuits and logic class please answer accordingly!
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