Homework 3.

Goals

• 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

1. [1 point each] Conversion : perform the following conversions.
   1. Convert 372 to binary
   2. Convert 1011101101₂ to decimal
   3. Convert 1011101101₂ to hexadecimal
   4. Convert 3ACD₁₆ to binary
2. [4 points] Describe the time complexity of a 4 bit ripple carry adder.
3. [4 points] Describe two problems using sign-magnitude to represent signed integers overcome by 2's compliment.
4. [1 point each] Represent each of the following in 4 bit two's complement.
   1. 3
   2. -3
   3. -7
   4. -8
5. [1 point each] The following represent numbers in 5 bit 2's compliment, provide the decimal sign-magnitude equivalent.
   1. 01010₂
   2. 10010₂
   3. 10000₂
   4. 11111₂
6. [4 points] Give an English description, truth table, mathematical expression and circuit symbol for the and operator.
7. [8 points] Show that ab+ac+bc = abc + abc + abc + abc.
   1. Using a truth table. Make sure that your rows are numbered in increasing order.
   2. Using a digital circuit.
8. [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.
   1. Build a truth table for this task
   2. Give the mathematical expression for your truth table.
   3. Build a circuit in digital to implement your expression.

Required Files

1. The word document with your answers.
2. One or more .dig files containing circuits you have created.

Submission