NumberSystems

NumberSystems - Understanding Binary and Hexadecimal...

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Understanding Binary and Hexadecimal Numbers In this paper, we will attempt to explain the binary and hexadecimal number systems and give examples of the conversion of a number from one number system to another. Only positive integers are considered. Introduction Computers store information as a series of ones and zeros. Each digit simulates a switch – “on” or “off”. When a variable is assigned a value such as decimal 12, the value stored will be 1100 in base 2, also known as binary. For readability, groups of binary digits are often grouped together in base 8, (i.e. octal) or in base 16 (hexadecimal). Hexadecimal numbers are more commonly used than Octal, so we will compare decimal numbers with binary and hexadecimal numbers Decimal Numbers: Base 10 In order to understand binary and hexadecimal numbers, it may be helpful to first look at the decimal or base 10 number system that we are all familiar with and use everyday. The decimal number 3725 states that there are 3 thousands plus 7 hundreds plus 2 tens plus 5 units. The valid numbers for each position are 0-9. When 1 is added to 9 in any position, a 10 cannot be placed in the same position so a one is carried over to the next (left) position and a zero is placed in the current position. Thus, 99 + 1 = 100. This might seem obvious in base ten, but it helps to think of this when we do a similar operation with a number in a different base number system. Where do the thousands, hundreds, tens, and unit columns come from? Mathematically each column is a power of ten starting with 10 to the zero power. Any number raised to the zero power is 1.
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NumberSystems - Understanding Binary and Hexadecimal...

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