Combinational logic

logic gates

By taking individual logic gates, we can combine them in a process knows as combinational logic to do increasingly more complex things. These logic gates are the foundation of computers. The bubble on top of some of the gates is an inverter, it inverts the previous signal to its opposite signal . So zero becomes one and one becomes zero .

Flip flops and latches

The set reset latch is made from two OR gates “or in this case Nor gates" and can be thought of as a one bit memory . This is because the output of each gate feeds into the input of the other Nor gate. This circuit when tethered together with others like it can be use to form memory registers.

Multiplexers

A multiplexer is a combinational circuit that selects binary information from many input lines to an output line. On this image the imputes are shown as A through S and the output is y. We select the values we want on the left with the variable A by electing different combinations of zeros and ones with the S or “selector” variables. So Value A0 is selected by the input S0=0 S1 = 0 S2=0 S3=0 or in simple terms 0000 = A0. Then 0001 =A1 and so on .

Decoders and encoders

Decoders and encoders help us refer to variables while using less values. So instead of referencing D0 as 1000000 we can say instead A1 A2 A3 or 000. Encoders allow us to translate more information using fewer wires. The decoder allows us to decode the information that was passed in by the encoder.

half adder full adder

The adder circuit takes two binary inputs and gives the sum as an output. It is made by tethering an xor gate as the sum bit and an And gate as the carry bit which carries the 1 if necessary. Full adders and carry ripple adders are adders tethered together to allow you to add large binary numbers.