TABLE OF CONTENTS Find the squares of 3-bit numbers.
Solution. With three bits a maximum of eight combinations are possible with decimal equivalents of 0 to 7. By squaring of the decimal numbers the maximum decimal number produced is 49, which can be formed with six bits. Let us consider three input variables are X, Y, and Z, and six output variables are A, B, C, D, E, and F. A truth table is prepared as in Figure 5.29 and Karnaugh maps for each of the output variables are shown in Figures 5.30(a)-(f).
| Input variables | Output variables | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Decimal Equivalent | X | Y | Z | Decimal Equivalent | A | B | C | D | E | F |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 1 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 1 |
| 2 | 0 | 1 | 0 | 4 | 0 | 0 | 0 | 1 | 0 | 0 |
| 3 | 0 | 1 | 1 | 9 | 0 | 0 | 1 | 0 | 0 | 1 |
| 4 | 1 | 0 | 0 | 16 | 0 | 1 | 0 | 0 | 0 | 0 |
| 5 | 1 | 0 | 1 | 25 | 0 | 1 | 1 | 0 | 0 | 1 |
