{"version":9,"randomSeed":"89dd26fb87ebe44e55649223e65b7a97","graph":{"viewport":{"xmin":-39.28694678330587,"ymin":-18.18499199552528,"xmax":13.899210618464544,"ymax":18.668951229254823}},"expressions":{"list":[{"type":"expression","id":"3","color":"#388c46","latex":"a=\\ln2","slider":{"max":"5702400"}},{"type":"text","id":"31","text":"Extract the first bit of x, returning (x >> 1, b(x)[0])"},{"type":"expression","id":"11","color":"#c74440","latex":"s\\left(x\\right)=\\left(\\operatorname{floor}\\left(\\frac{x}{2}\\right),\\operatorname{mod}\\left(\\operatorname{floor}\\left(x\\right),2\\right)\\right)"},{"type":"text","id":"33","text":"Extract the nth bit of x"},{"type":"expression","id":"25","color":"#000000","latex":"S\\left(x,n\\right)=\\operatorname{mod}\\left(\\operatorname{floor}\\left(\\frac{x}{2^{n}}\\right),2\\right)"},{"type":"text","id":"40","text":"Verify that converting to binary and back returns the original number"},{"type":"expression","id":"37","color":"#000000","latex":"\\sum_{n=0}^{100}2^{n}S\\left(a,n\\right)"},{"type":"text","id":"59","text":"Initial bit significance"},{"type":"expression","id":"56","color":"#c74440","latex":"I=-32"},{"type":"text","id":"61","text":"Number of bits used"},{"type":"expression","id":"57","color":"#2d70b3","latex":"C=64"},{"type":"expression","id":"46","color":"#c74440","latex":"b_{0}=\\left[I,I+1,...I+C-1\\right]"},{"type":"text","id":"49","text":"List of binary digits"},{"type":"expression","id":"47","color":"#2d70b3","latex":"b=S\\left(a,b_{0}\\right)"},{"type":"expression","id":"50","color":"#000000","latex":"y\\left(-2b\\left[\\operatorname{ceil}\\left(x\\right)-b_{0}\\left[1\\right]\\right]+1\\right)\\le1\\left\\{1\\le\\left|y\\right|\\le2\\right\\}","lines":false,"fillOpacity":"1"},{"type":"text","id":"52","text":"Byte groupings"},{"type":"expression","id":"53","color":"#fa7e19","latex":"y=\\left[-3,3\\right]\\left\\{0.2<\\operatorname{mod}\\left(x,8\\right)<7.8\\right\\}\\left\\{b_{0}\\left[1\\right]<x<b_{0}\\left[\\operatorname{length}\\left(b_{0}\\right)\\right]+1\\right\\}","lineOpacity":"1","lineWidth":"4"},{"type":"expression","id":"54","color":"#fa7e19","latex":"x=0.2+8b_{0}\\left\\{2.5<\\left|y\\right|<3\\right\\}\\left\\{x<b_{0}\\left[\\operatorname{length}\\left(b_{0}\\right)\\right]+1\\right\\}","lineOpacity":"1","lineWidth":"4"},{"type":"expression","id":"55","color":"#fa7e19","latex":"x=7.8+8b_{0}\\left\\{2.5<\\left|y\\right|<3\\right\\}\\left\\{x<b_{0}\\left[\\operatorname{length}\\left(b_{0}\\right)\\right]+1\\right\\}","lineOpacity":"1","lineWidth":"4"}]}}