Roman numerals look nice and go well with movie titles like Rambo III or Rocky IV.
However because of the different sized steps of I (1), V (5), X (10), L (50), C (100), D (500) and M (1000) they are not suitable for calculating numbers.
In ancient India probably in the third century a number system was developed that provides equal sized steps. In them including zero there are as many digits as the base of each system. In binary numbers there are the 1 and the 0. The octal system has seven numbers and the 0. The decimal system has nine numbers and the 0. And in the hexadecimal system has fifteen numbers and the 0. Such number systems are called polyadic number systems.
When counting up the digit with the lowest value increases until the value of the base is reached then the digit is reset and the next digit is added by one. If the binary system calculates 1+1 then the first digit starts again at 0 and the next digit is added by one. The result is 10 in the binary system and 2 in the decimal system. If 7+1 is calculated in the octal system then the first digit starts again at 0 and the next digit is added by one. The result is 10 in the octal system and 8 in the decimal system. If 9+1 is counted in the decimal system then the first digit starts again at 0 and the next digit is added by one. The result is 10 in decimal system. If F+1 is calculated in the hexadecimal system then the first digit starts again at 0 and the next digit is added by one. The result is 10 in the binary system and 16 in the decimal system.
Numbers with multiple digits can be converted from one number system to another number system. If the base of the input system is greater than the base of the output system then the number n in the input meter system is divided several times by the base of the output system and the remainder of the division is listed as a number in the output meter system. 11 is to be converted from the decimal system into the binary system. If 11 is divided by the base 2 then the result is 5 and the remainder is 1. If 5 is divided by the base 2 then the result is 2 and the remainder is 1. If 2 is divided by the base 2 then the result is 1 and the remainder is 0. If 1 is divided by the base 2 then the result is 0 and the remainder is 1. 11 in the decimal system becomes 1011 in the binary system by listing the remainders.
If the base of the input system is smaller than the base of the output system then the digits in the input system are multiplied by the base of the input system to the power of the position of the digits and added together. 1011 is to be converted from the binary system to the decimal system. The first digit (least significant bit LSB) 1 is multiplied by the base 2 high 0 and gives 1. The second digit 1 is multiplied by the base 2 high 1 and gives 2. The third digit 0 is multiplied by the base 2 high 2 and gives 0. The last digit (most significant bit MSB) 1 is multiplied by the base 2 high 3 and gives 8. Then the intermediate results 1, 2, 0 and 8 are added to give 11. 1011 in the binary system becomes 11 in the decimal system.
In ancient India probably in the third century a number system was developed that provides equal sized steps. In them including zero there are as many digits as the base of each system. In binary numbers there are the 1 and the 0. The octal system has seven numbers and the 0. The decimal system has nine numbers and the 0. And in the hexadecimal system has fifteen numbers and the 0. Such number systems are called polyadic number systems.
When counting up the digit with the lowest value increases until the value of the base is reached then the digit is reset and the next digit is added by one. If the binary system calculates 1+1 then the first digit starts again at 0 and the next digit is added by one. The result is 10 in the binary system and 2 in the decimal system. If 7+1 is calculated in the octal system then the first digit starts again at 0 and the next digit is added by one. The result is 10 in the octal system and 8 in the decimal system. If 9+1 is counted in the decimal system then the first digit starts again at 0 and the next digit is added by one. The result is 10 in decimal system. If F+1 is calculated in the hexadecimal system then the first digit starts again at 0 and the next digit is added by one. The result is 10 in the binary system and 16 in the decimal system.
Numbers with multiple digits can be converted from one number system to another number system. If the base of the input system is greater than the base of the output system then the number n in the input meter system is divided several times by the base of the output system and the remainder of the division is listed as a number in the output meter system. 11 is to be converted from the decimal system into the binary system. If 11 is divided by the base 2 then the result is 5 and the remainder is 1. If 5 is divided by the base 2 then the result is 2 and the remainder is 1. If 2 is divided by the base 2 then the result is 1 and the remainder is 0. If 1 is divided by the base 2 then the result is 0 and the remainder is 1. 11 in the decimal system becomes 1011 in the binary system by listing the remainders.
If the base of the input system is smaller than the base of the output system then the digits in the input system are multiplied by the base of the input system to the power of the position of the digits and added together. 1011 is to be converted from the binary system to the decimal system. The first digit (least significant bit LSB) 1 is multiplied by the base 2 high 0 and gives 1. The second digit 1 is multiplied by the base 2 high 1 and gives 2. The third digit 0 is multiplied by the base 2 high 2 and gives 0. The last digit (most significant bit MSB) 1 is multiplied by the base 2 high 3 and gives 8. Then the intermediate results 1, 2, 0 and 8 are added to give 11. 1011 in the binary system becomes 11 in the decimal system.
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