====== Lab Work 2 (Part 2) ======

====== Adders and Comparators ======

One of the most useful combinational logic circuit is an adder. It is the core component of any Arithmetic Unit - used in binary multipliers and even floating-point arithmetic units. Meanwhile, a comparator is useful as a decision making circuitry - it usually compares the magnitude of two binary values. 

====== Half-Adder ======

A half-adder sums two 1-bit values and provides two 1-bit values (sum and carry).

^  Half-Adder  ^^
|  Symbol  |  Truth Table  |
|  {{:archive:pgt104:hadd_block.jpg?direct&0x150|Block Symbol}}  |  {{:archive:pgt104:hadd_table.jpg?direct&0x150|Truth Table}}  |

//**Disclaimer**: The images above are extracted from resources available for Digital Fundamentals 11th Edition (Global Edition)//

====== Full-Adder ======

A full-adder sums three 1-bit values and provides two 1-bit values (sum and carry).

^  Full-Adder  ^^
|  Symbol  |  Truth Table  |
|  {{:archive:pgt104:fadd_block.jpg?direct&0x150|Block Symbol}}  |  {{:archive:pgt104:fadd_table.jpg?direct&0x150|Truth Table}}  |

//**Disclaimer**: The images above are extracted from resources available for Digital Fundamentals 11th Edition (Global Edition)//

====== Comparator ======

There are three possible output bits of a comparator (depending on application requirement): equality (''==''), less than (''<'') and greater than (''>'').

^  Comparator Output  ^  Description  ^
|  EQ (''=='')  | Output is at logic HI when the first value is exactly the same as the second value  |
|  LT (''<'')  | Output is at logic HI when the first value is less  than the second value  |
|  GT (''>'')  | Output is at logic HI when the first value is greater then the second value  |

Truth Table for a 1-bit Comparator:
^  A  ^  B  ^  EQ  ^  LT  ^  GT  ^
|  0  |  0  |  1  |  0  |  0  |
|  0  |  1  |  0  |  1  |  0  |
|  1  |  0  |  0  |  0  |  1  |
|  1  |  1  |  1  |  0  |  0  |

//**Note**: A 2-bit comparator cannot be built by simply cascading two 1-bit logic circuits.//

====== Things To Do ======

**THING 1** Build a 1-bit half-adder circuit and verify.

**THING 2** Build a 1-bit full-adder circuit using 2x1-bit half-adders. Verify. //Trivia: What is the least number of ICs (of 2-input logic gates) needed to implement this?//

**THING 3** (Optional?) Build a 2-bit adder and verify.

**THING 4** (Optional?) Construct a truth table for 1-bit subtractor. Build the circuit and verify.

**THING 5** (Optional?) Build a 4-bit ripple carry adder and verify.

**THING 6** (Optional?) Build a 4-bit carry look ahead (CLA) adder and verify.

**THING 7** Construct a truth table for 2-bit comparator (3 outputs). Get the Boolean expression for each output. Build the circuit and verify.

**THING 8** (Optional?) Build a 4-bit comparator (3 outputs) and verify.

//ask your instructor for more...//