WEBVTT

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In this video, we will understand the meaning of number systems and their bases.

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Describe decimal, binary, and hexadecimal systems with examples.

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Convert numbers between decimal, binary, and hexadecimal.

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What are number systems?

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A number system is a way of writing and representing numbers.

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It tells us what digits we can use and how their position changes the value.

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Decimal uses digits 0 to 9.

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Binary uses only 0 and 1.

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hexadecimal uses 0 to 9 and a to f.

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Decimal, binary, and hexadecimal.

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Each system has a different base, which is the count of unique digits it uses.

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This base is also called the radix.

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Decimal, base 10, everyday numbers.

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Binary, base 2, used inside computers.

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hexadecimal, base 16, compact way to represent binary.

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How positional value works.

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The position of a digit decides its value using powers of the base.

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This is called positional notation.

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Indesimal, 345 equals, 3 times 100, plus 4 times 10, plus 5 times 1.

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In binary, 1,11 equals 1 times 8, plus 0 times 4, plus 1 times 2, plus 1 times 1.

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Equals 11.

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In hexadecimal, 1A3 equals 1 times 256, plus 10 times 16, plus 3 times 1 equals 419.

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Conversions and uses.

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We can convert numbers between these systems using simple steps.

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Decimal, binary, divide by 2, or use powers of 2.

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Decimal, hexadecimal, divide by 16, or use powers of 16.

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Binary, hexadecimal, group binary digits and 4 bits.

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Used in QR codes, color codes, IP addresses, and digital clocks.

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Number systems form the foundation of computing.

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By understanding decimal, binary, and hexadecimal,

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we can see how numbers are stored, processed, and used in the digital world.