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
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I have already discussed clock arithmetic, modulo division, and number bases. We further our discussion in this post by learning how to change numbers from one base to another.
The number system that we are using everyday is called the decimal number system or the base 10 number system (deci means 10). It is believed that this system was developed because we have 10 fingers.
In the base 10 system, the digits are composed of 0 up to 9. Adding 1 to 9, the largest digit in this system, will give us 10. That is, we replace 9 in the ones place with 0, and add 1 to the tens place which is the next larger place value.
Another way to write a number in base 10 is by multiplying its digits by powers of 10 and adding them. For example, the number 2578 can be rewritten in expanded form as
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Our number system is called the decimal system (deci means 10) because we count in groups of 10’s. This is probably because we have 10 fingers. What do I mean when I said when we count in groups of 10?
Our number system has the digits 0 to 9, and then we when we reach the 10th number, we place 1 in the tens place 0 in the ones digit. In the decimal number system, 23 means that we have 2 tens and 3 ones. Similarly, the number 452 means that we have 4 groups hundreds (10 tens), 5 groups of tens and 8 ones. In fact, if we use the expanded notation, 452 is equal to
Notice that each number is multiplied by powers of 10. » Read more