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so letamp;#39;s talk a little bit about counting in binary or specifically you want to look at it in the context of making our truth tables so our truth tables are always listed with rows in binary order meaning that theyamp;#39;re counting properly with regards to how binary is counted so letamp;#39;s kind of start with a big example here letamp;#39;s say weamp;#39;ve got letamp;#39;s say weamp;#39;ve got a four variable truth table we want to have so weamp;#39;re gonna have a b c d or this is a 4-bit function right uses four inputs or four bits and letamp;#39;s uh letamp;#39;s start counting here so just like every number system we start off with zeros right this is zero zero zero zero and just like every other number system the next number is one so we start at zero when we go to one and just like if I were to say I give you Iamp;#39;m gonna give you that many dollars thatamp;#39;s $975 we know weamp;#39;ve got these zeros before it but they donamp;#39;t actually chang