1. 1 Ethics of Computing MONT 113G, Spring 2012 Session 5 Binary Addition

2. 2 Half adders and Full adders A half adder adds 2 binary digits and outputs a sum and a carry bit. A full adder adds 3 binary digits and outputs a sum and a carry bit. These can be used together to add 2 binary integers.

3. 3 Adding Binary Integers with Circuits a7 a6 a5 a4 a3 a2 a1 a0 + b7 b6 b5 b4 b3 b2 b1 b0 a0 b0 ½ adder s0 a1 b1 c0 full adder c1 full adder b2 a2 s1 s2 c2 etc. c0c1c2c3c4c5c6c7 s0s1s2s3s4s5s6s7

4. 4 Universal Building Blocks One can build any logical circuit with the following gates: 2 input AND gate 2 input OR gate Inverter In fact, one can build any logical circuit with just 1 type of gate: 2 input NAND

5. 5 Everything from NAND NOT a true z = a AND a b z = a  b true OR a b z = a V b true atrue output 01 1 1 1 0