# Homework 3.

### Goals

When you finish this homework, you should have:
- Convert between decimal, binary and hexadecimal
- Describe and use boolean expressions, truth tables and simple circuits.
- Discuss and evaluate methods of representing signed integers in binary

Please answer the following questions/perform the following tasks. Your answers should be placed in a word document. If the answer involves a circuit, implement this circuit in digital, and place a screen shot of the circuit in your answer word document.

- [1 point each] Conversion : perform the following conversions.
- Convert 372 to binary
- Convert 1011101101
_{2} to decimal
- Convert 1011101101
_{2} to hexadecimal
- Convert 3ACD
_{16} to binary

- [4 points] Describe the time complexity of a 4 bit ripple carry adder.
- [4 points] Describe two problems using sign-magnitude to represent signed integers overcome by 2's compliment.
- [1 point each] Represent each of the following in 4 bit two's complement.
- 3
- -3
- -7
- -8

- [1 point each] The following represent numbers in 5 bit 2's compliment, provide the decimal sign-magnitude equivalent.
- 01010
_{2}
- 10010
_{2}
- 10000
_{2}
- 11111
_{2}

- [4 points] Give an English description, truth table, mathematical expression and circuit symbol for the
`and`

operator.
- [8 points] Show that ab+ac+bc = abc + abc + abc + abc.
- Using a truth table. Make sure that your rows are numbered in increasing order.
- Using a digital circuit.

- [8 points] Construct a circuit to detect even parity in a three bit pattern. The parity of a bit pattern is found by summing the individual bits. If this sum is even, the pattern has even parity. For this exercise, 0 is even, so the bit pattern 000 has even parity.
- Build a truth table for this task
- Give the mathematical expression for your truth table.
- Build a circuit in digital to implement your expression.

### Required Files

Please submit a single tar or zip file containing:
- The word document with your answers.
- One or more .dig files containing circuits you have created.

### Submission

Submit the assignment to the D2L folder Homework 3 by the due date.