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In the previous post, we have learned how to change numbers form one base to other. In this post, we are going to discuss more examples of number bases particularly the two number systems used in computers: the binary and the hexadecimal system.
The Binary Number System
The binary number system has base 2 and only uses 1 and 0 as digits. The binary number 1101 in expanded form is
In Clock Arithmetic and Modular Systems, we have learned about a different number system, a number system whose largest digit is 12. We observed that in that system, we can only use the numbers 1 through 12. We also noticed that 12 acts as 0 since 12 added to any number is equal to that number. If we change 12 to 0, we can only use 0 through 11 as digits.
The number system that we use everyday, the decimal number system, uses 0 through 9 as digits. In the decimal number system, if we add 1 to the largest digit which is 9, we add 1 to the number on next place value and write 0. For example, 9 + 1 = 10 and 10 means that 1 tens and 0 ones. In the decimal number system, 325 means 3 tens squared (or hundreds), 2 tens and 5 ones. Using the expansion notation, we have » Read more