This blog will attempt to explain how to utilize the Octal numbering system, conversions between it and binary, and the various inputs/outputs of different logic gates.

Octal can represent eight different values (0-7). In order to find the Octal value of a number in binary, let's make an example of one byte, and then two bytes:

01101001 ~ 105

First we split the byte into groups of three bits starting right from left:

01 101 001

Next we have to pad to the left, since we're reading right to left, that way each groups retains the same value:

001 101 001

And find the integer accordingly:

001 = 1

101 = 5

001 = 1

So the integer 105 in binary equals the integer 151 in Octal. If we use two bytes:

01101001 01101001 ~ 105 105 (actually you can say 26,985 if you aren't associating any sort of digital device)

Split those up into sets of thee bits from right to left:

0 110 100 101 101 001

Add padding:

000 110 100 101 101 001

And find the integers accordingly:

0 6 4 5 5 1

You get the Octal integer 064551.

Logic gates are special devices made up of transistors. Transistors dictate the flow of electrons based on input conditions.

There are seven kinds of logic gates, some made up of others, that are widely used in electronic boards. These logic gates are:

NOT
AND
NAND
OR
NOR
XOR
XNOR

A NOT gate simply flips the input to its opposite; what we call an inverter. Give it a 1 and it spits out a 0 and vice versa.

An AND gate requires both inputs to be 1 in order for it to output a 1.

A NAND gate (NOT AND) only outputs a 1 if any input is 0.

An OR gate outputs 1 if at least one input is 1.

A NOR (NOT OR) gate outputs 1 only if both inputs are 0.

A XOR (EXCLUSIVE OR) gate outputs 1 only if one input is 1.

An XNOR (EXCLUSIVE NOT OR) gate outputs a 1 only of both inputs are the same.

Here's a chart: