Primary contact for this homework: Rebecca Lam [rjlam@cs.wisc.edu]

You must do this homework **in groups of two**. Please write the **full** name and the student id of each member on every pages and **staple multiple pages together.**

###
Problem 1 (2 points)

Write the decimal equivalents for these IEEE floating point numbers

- 00111111111000000000000000000000

1.75
- 10111110110000000000000000000000

-0.375

###
Problem 2 (5 points)

Given the logic equation Z = A OR B OR (NOT C)

- Draw the transistor level circuit for Z

Z = (A NOR B) NAND C

- Draw the gate-level circuit for Z using a
**minimal** number of NAND, NOT, and NOR gates

*Hint: Use DeMorgan's Law
###
Problem 3 (4 points)

Given the following transistor level circuit:

- Fill out the truth table for Z

A |
B |
Z |

0 |
0 |
0 |

0 |
1 |
1 |

1 |
0 |
1 |

1 |
1 |
1 |

- What is Z in terms of A and B

Z = A OR B

###
Problem 4 (5 points)

Given the logic equation Z = (A AND B) OR (B AND C) OR (A AND C)

- Fill out the truth table

A |
B |
C |
Z |

0 |
0 |
0 |
0 |

0 |
0 |
1 |
0 |

0 |
1 |
0 |
0 |

0 |
1 |
1 |
1 |

1 |
0 |
0 |
0 |

1 |
0 |
1 |
1 |

1 |
1 |
0 |
1 |

1 |
1 |
1 |
1 |

- Draw the gate-level circuit for Z using 2-input AND and OR gates

###
Problem 5 (4 points)

Given the logic equation Z = (A AND (NOT B)) OR ((NOT A) AND B)

- Fill out the truth table

A |
B |
Z |

0 |
0 |
0 |

0 |
1 |
1 |

1 |
0 |
1 |

1 |
1 |
0 |

- Is there a logic gate that implements this function? Give reasons for your answer.

Yes, the XOR gate.

###
Problem 6 (2 points)

Given an address size of 10 bits with 16 bits stored at each address, what is the total size of accessible memory(in bytes)?

2048 Bytes

###
Problem 7 (6 points)

Given the following truth table

- Draw the gate-level circuit using NOT gates and 3-input AND and OR gates.

- Convert the circuit of part a into a circuit that uses only NAND gates. *Hint: Use DeMorgan's Law

We use DeMorgan's Law on the OR gate and get the following:

A |
B |
C |
Z |

0 |
0 |
0 |
0 |

0 |
0 |
1 |
1 |

0 |
1 |
0 |
1 |

0 |
1 |
1 |
0 |

1 |
0 |
0 |
1 |

1 |
0 |
1 |
0 |

1 |
1 |
0 |
0 |

1 |
1 |
1 |
0 |

###
Problem 8 (2 points)

Using ASCII 8-bit, null-terminated string patterns, represent each of the characters in the string "Last Question!" using the hexadecimal value. (Only represent the characters between the quotation marks.)

4C 61 73 74 1 51 75 65 73 74 69 6F 6E 21 00