How I Invented Base64

Submitted by Ben Bryant on Tue, 2005-11-15 08:46.

Base64 is a way of storing any data as plain ASCII text. It looks like this:

LZPVtzlndhYFJQIDAQABMA0GCSqGSIb3DQEBAgUAA1kACKr0PqphJYw1j+YPtcIq
iWlFPuN5jJ79Khfg7ASFxskYkEMjRNZV/HZDZQEhtVaU7Jxfzs2wfX5byMp2X3U/
5XUXGx7qusDgHQGs7Jk9W8CW1fuSWUgN4w==

Look familiar? You'll see it in your e-mail source when your e-mail has attachments. How did I invent it? Well I didn't really, but before I knew base64 I came up with an encoding system I called "6-bit rollover" that turned out to be nearly identical to base64. It turns out that was not a momentous achievement because the beauty of base64 is how natural and simple it is. Here I am going to show how sensible base64 is by describing my discovery process, and giving you the quick round-up of everything you need to know to use base64.

Hex

Back in 1999, I needed to store a binary image in an XML document. There was no readily available function in Visual C++ or MSXML to do this. One common trick was to implement hex strings to hold binary values in strings with a few lines of code. Here is an example of 5 bytes represented in a Hex string:

48656C6C6F

Hex is pretty inefficient, taking two bytes of ASCII text for every byte of data, i.e. a 100% overhead in storage space. I figured there should be a way of using a larger variety of ASCII characters to result in using less storage space.

Stream of bits

The key is to picture the data as a stream of ones and zeros without byte boundaries, then you won't feel compelled to keep the chunks of bits from crossing those byte boundaries.

010101010101010101010101

Hex has one digit for every 4 bits in the data. The 4 bits represent a value from 0 to 15, so the characters 0123456789ABCDEF are used such that each character represents one of the values 0 to 15. If one character is used to represent every 4 bits, what if one character was used to represent every 5, 6 or 7 bits?

every 4 bits:

0101 0101 0101 0101 0101 0101...

every 5 bits:

01010 10101 01010 10101 0101...

every 6 bits:

010101 010101 010101 010101...

I felt it was important to stay within ASCII (values 0 to 127) because these only take 1 byte per character in UTF-8, and are generally immune to encoding corruption. The lowest ASCII codes are control characters including carriage returns and line feeds which I knew I didn't want to use as significant characters in my system. So 7 bits was out of the question since that would require all the values 0 to 127. However it was definitely possible to represent 6 bits as a single ASCII character, and this would yield a relatively efficient 33% overhead in storage space.

The base 64 alphabet

The next question was which characters to use. Hex uses 0-9 and A-F to represent the 16 different values in 4 bits. The problem now was to represent the 64 different values possible in 6 bits. Obviously you would want to use 0-9 and A-Z which is a total of 36 values. Then add the lower case letters for another 26, totaling 62 values.

Still 2 values short, and this is where a tough decision needs to be made because all of the other characters are punctuation signs which often have special meanings in various contexts. I happened to choose * (asterisk) and + (plus), but base64 uses + (plus) and / (slash), although there is a strain of base64 for URL and filename safety that uses - (minus) and _ (underscore). Base64 standardizes on an ordering as follows: uppercase, lowercase, numeric digits, and then the two additional characters.

Encode base64

To encode your data in base64, you preload a 64 digit character string and loop through your data 6 bits at a time, appending the appropriate digit to your result string by using the offset into your 64 digit character string. If you had a function called Get6Bits to retrieve a value for the next 6 bits in the buffer, your code would be this simple:

const char * pDigits = "A...Za...z0...9+/";
int nNextBits;
while ( Get6Bits(&nNextBits) )
  strResult += (char)pDigits[nNextBits];

If the number of bytes in the data is not divisible by 3, the 6 bits for the last base64 digit will be calculated as if there was an additional zero byte. Later when it is decoded, you will discard these extra 2 or 4 zero bits and (don't worry) you will always know the exact number of bytes that were in the original data.

One other thing about encoding base64 is that you are generally supposed to pad the result with equal signs to the edge of a 4 digit boundary (see the end of the top example of base64). There is no good reason for this that I can think of; just one of those artifacts of the old stodgy days of encoding when they invented little extra chores because they were so immersed in their own implementation scenario. In base64 there are 4 characters per 3 bytes of data and the way it turns out is there can only be 1 or 2 pad characters at the end since the first two characters are needed to complete the first of the 3 bytes. If you kept a count of base64 digits

nDigitCount

then your padding code might look like this:

int nRemainder = 4 - (nDigitCount % 4);
while ( nRemainder-- )
  strResult += '=';

Decode base64

To decode base64, preload an array to provide values or an error code for the corresponding digits at ASCII offsets, and tack 6 bits at a time onto your output buffer. The following pseudo-code relies on a function called Append6Bits which will append 6 bits at a time to your buffer unless the value is -1.

int aAsciiToBits[] = {-1...-1,62,-1,-1,-1,63,52...61,-1...-1,0,...,25,-1...-1,26...51,-1...-1};
for ( int n=0; strBase64[n]; ++n )
    Append6Bits( aAsciiToBits[strBase64[n]] );

The resulting output buffer length is rounded back to the the last byte for which all of the bits were supplied. In other words, if your data length is divisible by 3 bytes the bits will end up on a byte boundary. But if there is another byte, you will have 4 unused trailing bits, and if there are two other bytes, you will have 2 unused trailing bits.

References

The problem with base64 is that surprisingly it has no concise authoritative reference. RFC 3548 ("The Base16, Base32, and Base64 Data Encodings," 2003) is the best reference now and it summarizes the current status of the base64 standard. The two main references before that were buried in PEM (RFC 1421 "Privacy Enhancement for Internet Electronic Mail," 1993) and MIME (RFC 2045 "Multipurpose Internet Mail Extensions," 1996). Ignore the modified version of base64 for UTF-7 (RFC 2152, 1997), unless you are trafficking in UTF-7.

Line length

PEM and MIME differ on the number of characters per line: PEM says 64 and MIME says 76. But the line length doesn't matter since base64 stipulates to ignore non-significant characters like whitespace. It doesn't even need to be divided into lines at all; it can be just one continuous array of characters all on one line.

Other notes

Hex is case insensitive while base64 must be case sensitive. Base32 (5 bits per digit) which could theoretically be case insensitive, generally expects upper case, and has about 60% overhead. The overhead calculations I have given here do not include optional newline characters which add overhead too.

If I had started off by noting that the Hex encoding I have always used is also called "base16" encoding in the same way that "base64" uses a base 64 number system, I might have grasped what base64 was earlier than I did!

Ben Bryant's blog
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Good Article

Submitted by Paul Dix on Wed, 2005-11-16 20:59.

I've used library functions to take advantage of base64 encoding on a few occasions but never bothered to look into the details. It's always nice to find out what's happening behind the abstractions...

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Some treadmills have special features such as step count, heart rate monitors, amount of calories expended. I would recommend for a good walking treadmill that withstand regular use, you start somewhere in the $500 range.
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Every month you should check the belt on your treadmill to ensure it is aligned and that it seats securely. Also make sure you ask friends and family members that have had some of the same goals as you, in order to pick some equipment that will work with yours as well. WILD is not a poor choice in treadmills for many people, but if you are intent on a top quality, long lasting product, you may want to look further. Standard models usually come with more features such as a programmable consul that calculates heart rate or allows you to pick a heart rate and then adjust the resistance accordingly. You can tell the difference both by feel and by watching to see if the speed readout fluctuates. As a result, you`ll look taller, leaner and firmer much faster than you would if you did regular crunches.
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upright recumbent Magnetic bike While testing things out, pay attention to the console; is it easy to see? Easy to use? Make sure the motion is smooth, not jerky, and that the handrails are convenient. After all, the company first built its name by manufacturing road bikes. They both require a minimum of equipment and accessories to perform too. Sometimes you`ll find comparable models and the only difference is that one has a rebate program and another doesn`t. By taking the time to research you can save yourself a lot of money.
Incline Adjustment: There`s a variety of ways to adjust the incline of a home treadmill, from the automatic incline which changes depending upon your heart rate, to pushing a bottom on the console, to the less sophisticated methods of a manual hand crank or manually setting pins. Look into extended warranties. Exposure to such elements will damage certain crucial parts of your equipment. If you want your treadmill to last, be sure to check the belt for stretching or cracking.
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Price: Keep in mind, you get what you pay for. Just feel free to click on the links provided here and learn from our articles and tips on how you can get in shape and stay there using a variety of home fitness workouts and methods. One thing to remember though is before you start any rigorous workout program, check with your doctor to make sure your body is ready for it. And ease yourself into it going light for the first few sessions. rating can be a deceptive hoax if the treadmill manufacturer has not gone to the expense of using the right kind of motor for the job. What you want is both high continuous-duty horsepower and high torque at low revs. Less power is required at higher speeds, therefore more power is needed at start-up and walking speeds. User weight shouldn`t matter on a treadmill that uses a motor capable of high torque at low speeds. A good treadmill will dead-start well over 1,000 pounds. Some treadmills will actually use higher torque at higher speeds to raise the horsepower (over 6 m.p.h. where the user actually starts helping the belt along with foot motion), but good engineering puts torque where it is needed most, around 0.5 to 4 m.p.h. More power means a smoother walk or run without hesitations and motor resistance. In fact, there is a much smaller amp draw on the motor when initializing torque, as compared to a higher consumption of wattage when a motor is working harder to maintain faster speeds - or its maximum use of horsepower potential. This results in a longer lasting and cooler running motor.
Motor Controller
The treadmill motor will be controlled by an electrical power board, which regulates the positive and negative electrical currents to the motor. You should consider motor controller included in treadmill comparison. Because it can affect the life of the treadmill. Due to the technical language used in explaining what each does, we suggest asking a salesperson responsible for your treadmill of interest about this feature. Simply put, a PWM board will provide much more DC voltage than an SCR board by rectifying an alternating current (AC) into pure direct current (DC) voltage. SCR chops a 60-cycle alternating current 60 times per second, while a PWM will chop it about 16,000 times. (AC voltage is a constant change of positive/negative current 60 times per second, which is a cycle.) PWM boards result in a much quieter motor due to less electrical hum, and less service because they do not require chokes and filters. Higher pure DC voltage in PWM boards means a stronger current and about half the amp draw, resulting in higher tolerance to heavier users and lower electrical costs. PWM makes for less heat and therefore leads to: extended motor performance and longer brush life; easier torque boost adjustment; the use of heavier flywheels; and enough power to dead-start a heavier user weight. PWM boards are the standard in quality motor controllers.
Speed
Most treadmills run from 0 to 10 M.P.H. According your need, speed is included treadmill comparison.though some designed specifically for walking may have more limited speeds. The right treadmill for you will match your own pace, whether fast or slow. Starting speed is a more important issue, and we recommend a safe starting speed of 1 M.P.H. or less. It`s not that you will be walking that slow, but starting speeds of more than a mile per hour are often too fast for most motors and may result as a jerk when the belt is started.
Fit
Make sure from walking on a treadmill that there is more than enough room on the belt for your longest stride. Narrow or short tread belts are symptomatic of a high-friction bed. We recommend a belt no less than 16 inches wide. Make sure that you can reach and read the monitor without walking onto the motor housing. Be careful of stepping off the end, as well. Quality belts shouldn`t require frequent maintenance, whereas low quality belts need to be regularly lubricated, otherwise they stick to the deck. Make sure that belts which require adjustment for tracking and tension can easily be adjusted by you.
Deck
It has been argued by many that a quality deck is the single most important component of a quality treadmill. Treadmills fail due to heat, and better decks operate at low temperatures. Quality treadmills have pretreated decks requiring very little maintenance other than wiping off dust. Other than that, quality decks should need no substantial maintenance. Listen for a deck that makes little noise against the belt when exercising. Avoid decks comprised simply of plastic over wood or particleboard painted black. A good deck will be made from layers of different specialty material for durability and longevity. A permanent wax compound is preferable to compressed fiberboard in deck construction because this greatly reduces friction. The best deck and belt combination is a dry one. If in doubt, ask about whether or not to lubricate the deck with silicone spray, and then follow the manufacturer`s directions during the warranty period.
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of your feet. Resilience is included in treadmill comparison. It will affect your comfortable when you run on the treadmill. It helps to relieve the stress on your knees and ankles. Generally, the lower the impact, the better. Different treadmills employ different means of resilience, whether flexible or cushioned deck construction, or shock absorption suspension systems. Most will have a built-in give, allowing it to yield to the impact of your stride. Whatever the feature, a treadmill shouldn`t be too cushioned or bouncy. The majority of treadmills have better resilience than asphalt. A good pair of shoes and an anti-static mat will provide enough shock absorption.
Rollers
Of course, roller is also considered to treadmill comparison. Roller size is better if about 2 or more inches in diameter. The reason for this is that the belt is able to run with less tension due to contact with a larger surface area, which results in a longer life to both the belt and the roller bearings. Larger rollers turn more slowly at all speeds, which also prolongs bearing life. Larger rollers mean the use of larger bearings, which can handle a larger load capacity. There is less stress on the belt when forced around larger rollers, and less flex stress results in cooler temperatures on the polyester fibers of the belt, in turn, leading to less wear than small rollers with more belt flex, higher temperatures, and tighter belt tension. At cooler temperatures the belt coating last longer and thus prevents excess friction. There is also more overall strength to the treadmill with larger rollers simply because they require larger axles. Steel rollers are preferable to aluminum because aluminum rollers can oxidize and may form a grinding material that acts as sandpaper on the belt. Solid rollers are much better than hollow rollers.
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pneumatic or gas shocks, and manual cranks.Incline is in treadmill comparison. It is according your need to decide whether to choose treadmill with incline. Quality incline should be quiet and shouldn`t allow the treadmill to wobble at high elevations. Electric incline with a worm screw is ideal, though because it uses a separate motor the price is then affected by another couple hundred dollars. If you do prefer electric incline then make sure the motor doesn`t strain with one or two people on the treadmill, which would indicate a weak motor. You will generally find manual cranks on lower-end treadmills to keep production costs down. Though any of these means of incline are just fine, make sure the control is located on the monitor console where you can adjust it while exercising. Most quality treadmills will incline to 10%, and though you want maximum incline to help attain to your target heart rate, too much incline may easily lead to injury. Most users don`t go above 10%.
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Handrail location is up to the user. Whether one or two side rails or a handlebar on the front of the monitor console, they should be sturdy and out of the way of swinging arms. They are mostly used for balance, so make sure your treadmill has reachable and sturdy bars with comfortable grips. It is not necessary to hold the handrails, and you will get a more natural feel if you walk upright at your normal speed, just as if you were outside. You can carry a couple of small weights to give yourself an upper body workout while you walk.
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For health, you buy treadmill. So safety is in your mind about treadmill comparison.Because motorized treadmills are a moving, machine certain safety precautions must be included as standard features, including an emergency shut-off that is easily accessible, the ability to limit incline and speed, a gradual start and stop, and accessible hand rails for both runners and walkers. A safe starting speed is 1 M.P.H. or less. It`s also good for a treadmill to have its own circuit breaker to prevent the motor and electronics from burning up in case of power problems. The use of extension cords should be avoided, and the power supply must be grounded. An anti-static mat will help keep your machine in position, as well as eliminate static buildup in the tread belt. A mat will help protect your floor from dirt, sweat, scratches and dents.
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