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A Bit Can Have How Many Different Values

author
Brent Mccoy
• Sunday, 06 December, 2020
• 7 min read

For example, if n=9, then how manydifferentvaluescan be represented in 9 binary digits (bits)? My thinking is that if I set each of those 9 bits to 1, I will make the highest number possible that those 9 digits are able to represent.

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(Source: www.thepropertyvoice.net)

Contents

Sam Stephens SamStephens5,51355 gold badges3232 silver badges4444 bronze badges Okay, since it already “leaked”: You're missing zero, so the correct answer is 512 (511 is the greatest one, but it's 0 to 511, not 1 to 511).

There are different ways to encode binary numbers. For 9 bits, the ranges and the amount of numbers that can be represented will differ depending on the system used.

In this section, we'll learn how bits and bytes encode information. The bit stores just a 0 or 1: it's the smallest building block of storage.

ASCII is an encoding representing each typed character by a number Each number is stored in one byte (so the number is in 0.255) A is 65 B is 66 an is 96 space is 32 “Unicode” is an encoding for mandarin, Greek, Arabic, etc. Each letter is stored in a byte, as below 100 typed letters takes up 100 bytes When you send, say, a text message, the numbers are sent Text is quite compact, using few bytes, compared to image etc.

One byte works well for individual characters, but computers are also good at manipulating numbers. Integers are typically stored with either 4 or 8 bytes 4 bytes can store numbers between -2147483648 and 2147483647 8 bytes can store numbers between -9223372036854775808 and 9223372036854775807 Adding in binary is just like normal addition with carrying But when you run out of bits you can 't carry any more Leftmost bit indicates sign, so carrying to the leftmost bit changes a number from positive to negative.

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(Source: www.slideshare.net)

A bit (short for binary digit) is the smallest unit of data in a computer. For more information, check the Wikipedia with the title “Radix”.

Also notice that each time we add another binary digit we double the possible values. So, a binary number with 50 digits could have 1,125,899,906,842,624 different values.

Or to put it another way, it could show a number up to 1,125,899,906,842,623 (note: this is one less than the total number of values, because one of the values is 0). There is an old Indian legend about a King who was challenged to a game of chess by a visiting Sage.

(By the way, in the legend the Sage reveals himself to be Lord Krishna and tells the King that he doesn't have to pay the debt at once, but can pay him over time, just serve rice to pilgrims every day until the debt is paid off.) Lastly, let us look at the special relationship between Binary and Hexadecimal.

So, when people use computers (which prefer binary numbers), it is a lot easier to use the single hexadecimal digit rather than 4 binary digits. The world's first stored program electronic computer, the Manchester Baby, used a 32- bit architecture in 1948, although it was only a proof of concept and had little practical capacity.

(Source: www.sedris.org)

It held only 32 32- bit words of RAM on a Williams tube, and had no addition operation, only subtraction. Memory, as well as other digital circuits and wiring, was expensive during the first decades of 32- bit architectures (the 1960s to the 1980s).

Older 32- bit processor families (or simpler, cheaper variants thereof) could therefore have many compromises and limitations in order to cut costs. This could be a 16- bit ALU, for instance, or external (or internal) buses narrower than 32 bits, limiting memory size or demanding more cycles for instruction fetch, execution or write back.

In this context, the term came about because DOS, Microsoft Windows and OS/2 were originally written for the 8088/8086 or 80286, 16- bit microprocessors with a segmented address space where programs had to switch between segments to reach more than 64 kilobytes of code or data. Furthermore, programming with segments tend to become complicated; special far and near keywords or memory models had to be used (with care), not only in assembly language but also in high level languages such as Pascal, compiled BASIC, FORTRAN, C, etc.

The former possibility exists for backward compatibility and the latter is usually meant to be used for new software development. 32- bit -per-channel images are used to represent values brighter than what RGB color space allows (brighter than white); these value scan then be used to more accurately retain bright highlights when either lowering the exposure of the image or when it is seen through a dark filter or dull reflection.

To figure out how many unique values can be represented in x number, simply do 2 to the power of x. Each bit is capable of having 2 values 0 and 1.

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(Source: boldomatic.com)

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Sources
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2 www.ovationriding.com - https://www.ovationriding.com/horse-girths
3 www.colindangaard.com - https://www.colindangaard.com/shop-cinches-girthing-systems/neoprene-girths
4 www.centralsaddleandtack.com - http://www.centralsaddleandtack.com/products/girths/roping-girths/
5 www.cinchesdownunder.com - https://www.cinchesdownunder.com/products/traditional-combination-stock-saddle-girth/
6 www.tackshop.co.nz - https://www.tackshop.co.nz/saddles-accessories-55/girths.html
7 firstthought.1.ekm.shop - https://firstthought.1.ekm.shop/girths-64-c.asp
8 westernshoppe.com - https://westernshoppe.com/product-category/saddles/girths/page/2/
9 www.horsenation.com - https://www.horsenation.com/2015/04/16/product-review-the-total-fit-shoulder-relief-dressage-girth/