Introduction

In this lab, we will look at how two voltages levels can be used to perform arithmetic. By utilizing just two voltage levels, a "high" and a "low", we create a binary system. The binary system is "a language" used to create mathematical formulas, such as algebraic equations, but also logical expressions. This branch of mathematics is called Boolean algebra, introduced by George Boole, in which the values of the variables are either "true" or "false" (also called "high" or "low"; "1" or "0"). The various terms for the two states will be used interchangeably. The implementation of Boolean algebra with circuitry and programming is called digital logic. Boolean algebra is basis for the development of digital electronics.

In this lab we will build a one-bit full-adder, which adds three data bits, which include data bits \(x\) and \(y\), and a carry bit \(z\). The output of the adder will be a one-bit result and a one-bit carry.

Note: The name "full-adder" comes from the fact that it can be constructed by combining two half-adders, each of which adds only two bits.