Question

Create a truth table according to these specifications: There are 4 input bits, x3, x2, x1, x0, and 3 output bits, s2, s1, s0. The 3-bit output is the largest number of consecutive 1's in the 4 input bits. (x3 is the most significant bit of the input, and s2 is the most significant bit of the output.) For example, input 0000 gives output 000 (no 1's), inputs 0001 and 0101 give output 001, inputs 0011 and 0110 give output 010, input 1110 gives output 011, etc. Show all 16 rows of the table clearly. (You can write this out neatly in plain text; don't worry about using tables in a word processor.) b) Refer to Chapter 6 Slide 9, where we filled out the truth table for the 2-bit adder. We also wrote out a logical expression for the s0 bit, following a sum of products approach. For the s0 bit of the new circuit, follow the same procedure and write out the logical expression.

Answer 1

Here is the truth table for the circuit:

| x3 | x2 | x1 | x0 | s2 | s1 | s0 |

|----|----|----|----|----|----|----|

| 0 | 0 | 0 | 0 | 0 | 0 | 0 |

| 0 | 0 | 0 | 1 | 0 | 0 | 1 |

| 0 | 0 | 1 | 0 | 0 | 0 | 1 |

| 0 | 0 | 1 | 1 | 0 | 1 | 0 |

| 0 | 1 | 0 | 0 | 0 | 1 | 1 |

| 0 | 1 | 0 | 1 | 0 | 1 | 1 |

| 0 | 1 | 1 | 0 | 1 | 0 | 0 |

| 0 | 1 | 1 | 1 | 1 | 0 | 0 |

| 1 | 0 | 0 | 0 | 1 | 0 | 1 |

| 1 | 0 | 0 | 1 | 1 | 0 | 1 |

| 1 | 0 | 1 | 0 | 1 | 1 | 0 |

| 1 | 0 | 1 | 1 | 1 | 1 | 0 |

| 1 | 1 | 0 | 0 | 1 | 1 | 1 |

| 1 | 1 | 0 | 1 | 1 | 1 | 1 |

| 1 | 1 | 1 | 0 | 1 | 1 | 1 |

| 1 | 1 | 1 | 1 | 1 | 1 | 1 |

To write