Numeral systems

Exponential-Golomb coding

An exponential-Golomb code (or just Exp-Golomb code) is a type of universal code. To encode any nonnegative integer x using the exp-Golomb code: 1. * Write down x+1 in binary 2. * Count the bits written, subtract one, and write that number of starting zero bits preceding the previous bit string. The first few values of the code are: 0 ⇒ 1 ⇒ 1 1 ⇒ 10 ⇒ 010 2 ⇒ 11 ⇒ 011 3 ⇒ 100 ⇒ 00100 4 ⇒ 101 ⇒ 00101 5 ⇒ 110 ⇒ 00110 6 ⇒ 111 ⇒ 00111 7 ⇒ 1000 ⇒ 0001000 8 ⇒ 1001 ⇒ 0001001... In the above examples, consider the case 3. For 3, x+1 = 3 + 1 = 4. 4 in binary is '100'. '100' has 3 bits, and 3-1 = 2. Hence add 2 zeros before '100', which is '00100' Similarly, consider 8. '8 + 1' in binary is '1001'. '1001' has 4 bits, and 4-1 is 3. Hence add 3 zeros before 1001, which is '0001001'. This is identical to the Elias gamma code of x+1, allowing it to encode 0. (Wikipedia).

Video thumbnail

How to Solve an Exponential Equation with Three Exponentials with Exponents as Logarithms

How to Solve an Exponential Equation with Three Exponentials with Exponents as Logarithms If you enjoyed this video please consider liking, sharing, and subscribing. Udemy Courses Via My Website: https://mathsorcerer.com My FaceBook Page: https://www.facebook.com/themathsorcerer There

From playlist Exponential Equations

Video thumbnail

Solving an exponential equation using the one to one property 16^x + 2 = 6

👉 Learn how to solve exponential equations. An exponential equation is an equation in which a variable occurs as an exponent. To solve an exponential equation, we isolate the exponential part of the equation. Then we take the log of both sides. Note that the base of the log should correspo

From playlist Solve Exponential Equations with Logarithms

Video thumbnail

Planing Sequences (Le Rabot) - Numberphile

Featuring Neil Sloane from the OEIS - and his carpenter's plane. Mandelbrot papers offer: https://www.patreon.com/posts/52011294 More links & stuff in full description below ↓↓↓ More Neil Sloane videos: http://bit.ly/Sloane_Numberphile The OEIS: https://oeis.org Discuss this video on Br

From playlist Neil Sloane on Numberphile

Video thumbnail

The Pentomino Puzzle (and Tetris) - Numberphile

Featuring Alex Bellos on Polyominoes. See the accompanying coin hexagon video: https://youtu.be/_pP_C7HEy3g More links & stuff in full description below ↓↓↓ More Alex Bellos videos: http://bit.ly/Bellos_Playlist Related Bellos books on Amazon... US links Can You Solve My Problems: https:

From playlist Alex Bellos on Numberphile

Video thumbnail

Using the inverse of an exponential equation to find the logarithm

👉 Learn how to convert an exponential equation to a logarithmic equation. This is very important to learn because it not only helps us explain the definition of a logarithm but how it is related to the exponential function. Knowing how to convert between the different forms will help us i

From playlist Logarithmic and Exponential Form | Learn About

Video thumbnail

Erika Berenice Roldán Roa - Polyominoes with Maximally Many Holes - G4G13 Apr 2018

In 1953 Solomon W. Golomb defined a polyomino as a rook-wise, connected subset of squares of the infinite checkerboard. The first polyomino puzzles were tiling problems. Most of the time in tiling problems one restricts to simply-connected polyominoes (i.e., polyominoes without holes). But

From playlist G4G13 Videos

Video thumbnail

Solve an exponential equation using one to one property and isolating the exponent

👉 Learn how to solve exponential equations. An exponential equation is an equation in which a variable occurs as an exponent. To solve an exponential equation, we isolate the exponential part of the equation. Then we take the log of both sides. Note that the base of the log should correspo

From playlist Solve Exponential Equations with Logarithms

Video thumbnail

Six Sequences - Numberphile

Which of these number sequences do you like best? Vote at http://bit.ly/IntegestVote The extra bit of footage is at: http://youtu.be/p-p7ozCnjfU More links & stuff in full description below ↓↓↓ This video features Tony Padilla from the University of Nottingham: https://twitter.com/DrTonyP

From playlist Tony Padilla on Numberphile

Video thumbnail

Learn the basics for solve an exponential equation using a calculator

👉 Learn how to solve exponential equations. An exponential equation is an equation in which a variable occurs as an exponent. To solve an exponential equation, we isolate the exponential part of the equation. Then we take the log of both sides. Note that the base of the log should correspo

From playlist Solve Exponential Equations with Logarithms

Video thumbnail

Using one to one property when exponents do not have the same base, 25^(x+3) = 5

👉 Learn how to solve exponential equations. An exponential equation is an equation in which a variable occurs as an exponent. To solve an exponential equation, we isolate the exponential part of the equation. Then we take the log of both sides. Note that the base of the log should correspo

From playlist Solve Exponential Equations without a Calculator

Video thumbnail

Tomas Rokicki - Large Golomb Rulers - G4G12 April 2016

Does a subquadratic Golomb Ruler exist for any number of marks? We share our exploration of this question. We have shown there are always subquadratic rulers through 492,115 marks, but the existing constructions do not find any for 492,116 marks.

From playlist G4G12 Videos

Video thumbnail

Solving exponential equations using the one to one property

👉 Learn how to solve exponential equations. An exponential equation is an equation in which a variable occurs as an exponent. To solve an exponential equation, we isolate the exponential part of the equation. Then we take the log of both sides. Note that the base of the log should correspo

From playlist Solve Exponential Equations with Logarithms

Video thumbnail

Raymond Hall - @physicsfun: Social Media as a Museum of Science and Math - G4G14 Apr 2022

@physicsfun: Social Media as a Museum of Science and Math (and A Recent Path Down a Rabbit Hole with Pentomino Tilings) In the spirit of Martin Gardner I curate a museum of science and mathematics on the social media platform Instagram that features short videos (60 seconds or less) of ma

From playlist G4G14 Videos

Video thumbnail

Rewriting a exponential equation to solve using one to one properties (2/3)^x = 4/9

👉 Learn how to solve exponential equations. An exponential equation is an equation in which a variable occurs as an exponent. To solve an exponential equation, we isolate the exponential part of the equation. Then we take the log of both sides. Note that the base of the log should correspo

From playlist Solve Exponential Equations without a Calculator

Video thumbnail

Using one to one properties to solve an exponential equation

👉 Learn how to solve exponential equations. An exponential equation is an equation in which a variable occurs as an exponent. To solve an exponential equation, we isolate the exponential part of the equation. Then we take the log of both sides. Note that the base of the log should correspo

From playlist Solve Exponential Equations without a Calculator

Video thumbnail

USC Living History Project - Solomon Golomb (2014)

Solomon Golomb, Distinguished Professor of Electrical Engineering and Mathematics, Viterbi School of Engineering. Interviewed by Alexander A. Sawchuk, Professor in the Ming Hsieh Dept of Electrical Engineering, Viterbi School of Engineering.

From playlist Interviews

Video thumbnail

Anany Levitin - Polyomino Puzzles and Algorithm Design Techniques - G4G13 April 2018

The presentation – in memoriam of Solomon Golomb – shows how polyomino puzzles can be used for illustrating different algorithm design techniques

From playlist G4G13 Videos

Video thumbnail

Learn how to solve an exponential equation 2^(x-3) = 32

👉 Learn how to solve exponential equations. An exponential equation is an equation in which a variable occurs as an exponent. To solve an exponential equation, we isolate the exponential part of the equation. Then we take the log of both sides. Note that the base of the log should correspo

From playlist Solve Exponential Equations without a Calculator

Related pages

Elias gamma coding | Elias delta coding | Elias omega coding | Dirac (video compression format)