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the most popular number system used

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today

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is the decimal system where the base is

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10.

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however for most of history another

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number system was more commonly used

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the sexagesimal system which has the

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base of 60.

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it was the preferred number system in

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astronomy in particular

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this system had been used by the

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babylonians

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during the 15th century bc and later by

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the greeks

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medieval islamic mathematicians although

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familiar with the decimal system

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most often use the sexagesimal system

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which they adapted and improved

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from the previous civilizations in this

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hexadecimal system

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one unit is 60 instead of 10. thus

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in this system we need 60 digits 0

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through 59

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while in the decimal system we only need

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10.

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an example of the use of this

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hexadecimal system in our everyday lives

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is the clock where 1 hour is divided

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into 60 minutes

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and one minute is divided into 60

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seconds

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after inheriting the sexagesimal system

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from babylonians and greeks

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islamic scholars improved and clarified

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the system

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similarly to the decimal number system

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after the contributions of islamic

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scholars

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the sexagesimal system essentially

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became the system we use today

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the babylonian system was used in

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mesopotamia

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around the year 2000 bc it was a

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positional system

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in which successive places of a numeral

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represent

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the success of power or positive

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integers of the base

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60 so it treated whole numbers and

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fractions

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in a unified manner the system only had

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two

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ciphers and no special mark for the

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unit's place

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leading to confusion because position

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values are not

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explicitly specified there was no way to

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distinguish between possible values

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represented by a given set of symbols in

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this

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system for example these two

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ciphers could represent either 1 and 1 3

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or 80 or many other possible values

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after the second century bc greek

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astronomers sought to alleviate some of

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the confusion

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created by only having two ciphers by

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using the 27 letters of the greek

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alphabet

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to represent numbers thus while these

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two ciphers could have indicated

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one-third in the babylonian system

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greeks simply used the letter k the

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babylonian and greek systems were

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refined by islamic mathematicians

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like the greek system islamic

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mathematicians used

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28 letters of the arabic alphabet as

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ciphers

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however while both the babylonians and

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the greeks

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lacked a differentiation of place values

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islamic mathematicians easily divided up

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the units

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and named the positions both in the

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fractional and whole

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part positive powers went from

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degrees first elevenths second elevates

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and so on

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while negative powers were called

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minutes seconds thirds

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etc each unit was comprised of 60

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of the previous unit

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the base of a sexadecimal number is 60

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thus a digit n in the unit's place

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called

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degrees is equal to the decimal number n

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times 60 to the power of zero

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decreasing from the units are the

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minutes seconds

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thirds etc the digit n in minutes place

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is equal to n divided by 60

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and seconds is equal to n divided by 60

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squared

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increasing from the units are the first

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elevates second elevates

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etc first elevates is equal to

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n times sixty to the power of one while

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second elevates is equal to n times

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sixty to the power of two

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thus the conversion chart for decimal to

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hexadecimal

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looks something like this

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let's look at a sexagesimal number in

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more detail

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here we have the number one second

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elevate

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six first elevates three degrees 15

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minutes and nine seconds

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using the chart we know that the value

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of this number is

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one times sixty squared plus six times

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sixty

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plus three times sixty to the power of

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zero plus fifteen divided by sixty

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plus nine divided by six c squared

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in order to convert the sexadecimal

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number to decimal

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we simply multiply all of the numbers

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with their bases

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and add them all together again

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this would be 3600 plus 360

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plus 3 plus 0.25

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plus 0.0025 all equaling to

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3963

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the cipherization and increased

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organization of the ancient sexagesimal

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system by medieval islamic

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mathematicians

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was a tremendously useful contribution

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that perfected

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the system