Homework 4

When you complete this homework you should

• Be able to use TKGate to implement basic circuits.
• Understand how to translate simple problem descriptions into solutions implemented in basic logic.

All circuits should be implementd using only and, or and not gates.

1. [3 points] Develop a two input logical equivalence tester.
   1. Derive a truth table which for a circuit that takes two inputs, a and b, and produces a 1 when the inputs are equal and a 0 when the inputs are not equal.
   2. Using the circuit from part A, develop a boolean equation which produces a 1 if the two variables are the same and a 0 otherwise.
   3. Using only and, or and not gates, create a circuit in TKGate which implements the equation and circuit in the previous parts.
2. [3 points] Show that DeMorgan's law: a+b = a · b is true
   1. Develop a two input circuit for a+b
   2. Develop a two input circuit for a · b
   3. Use the circuits from 2A and 2B to provide input to the circuit developed in 1C.
3. [4 points] Assume a number X consists of 3 bits, x₂, x₁ and x₀. Write a logical function and construct a circuit in TKGate to
   1. Detect if X is 0, or all input is 0. If all input is 0, output a 1, otherwise output a 0.
   2. Detect if X is negative in 3 bit two's complement representation. If the number is negative, output a 1, otherwise output a 0.
4. [2 pionts] Develop a circuit which given a 4 bit WOMBAT op-code, determines if the instrucion is a math-class (add, subtract, multiply, divide) instruction. Output a 1 if the opcode indicates a math instruction and a 0 otherwise.