Number base systems are the foundation of how we represent and manipulate numbers in different formats. They're crucial in computing, where and reign supreme. Understanding these systems helps us grasp how computers process data and perform calculations.
Converting between bases is a key skill in working with different . Whether you're using place value methods or repeated division, mastering these techniques opens doors to understanding computer science and digital electronics on a deeper level.
Number Base Systems
Number base conversion methods
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for converting from base 10 to another base
Expresses the base 10 number as a sum of powers of the new base multiplied by their respective coefficients
Coefficients are determined by the digits in the new base representation
Example: 7510=7×81+5×80=1158
Place value method for converting from another base to base 10
Multiplies each digit in the number by the base raised to the power of its place value position (rightmost digit has a place value of 0, increasing by 1 for each position to the left)
Sums the resulting products to obtain the base 10 equivalent
Example: 11012=1×23+1×22+0×21+1×20=1310
for converting from base 10 to another base
Divides the base 10 number by the new base repeatedly until the becomes 0
Collects the remainders in reverse order to form the digits of the new base representation