Blog #4: "Can I have your digits?"

Numeral / Number Systems

(all images are from Google Images, unless stated otherwise.)

     Well, numbers are part of our lives. Before coming up with 1, 2, 3, to infinity, our ancestors, the Romans, Egyptians, and other ancient mathematicians developed number systems that I'm sure we are familiar with, or we have encountered in school.

Roman Numerals

Egyptian Numerals

Unary Number System

     Numeral systems are notations of expressing numbers. Do you remember the methods of counting you used to do?

     I often use the unary numerals, or simply tallying. When counting in small digits, I use my fingers. When I count large digits, I group them. For example, when I count my coins from my piggybank, I group them in tens so I could easily count.

Our lesson for the week's meeting - Decimal, Binary, Octal, Hexadecimal

Decimal Number System (base 10)

     The counting we do in everyday life, though not all of us may know it, or put attention to it, or even give a thought about what it is, is called the DECIMAL NUMBER SYSTEM. The decimal number system makes use of base 10. Now what am I talking about? Base 10 means 10 digits in a place value of a position. In the first position, or in the ones place, the 10 digits are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. When you reach 9, you go back to 0 in the ones place, and then add 1 in the tens place. When you reach 9 again in the ones place, you go back to 0, then add another 1 in the tens place, making your count 20.

from http://drstienecker.com/tech-332/1-numbering-systems-and-conversions/

     Binary, octal, and hexadecimal are the number systems used by our computer. Simply put, those are the "languages" of the computer. Since we "talk" in decimal, we must know how to convert it to binary, octal, and hexadecimal so the computer will understand our command.

Binary Number System (base 2)

     We all know the famous binary digits. It is the smallest unit of data in a computer. Binary is composed of 2 digits (base 2): 0 and 1, or "on" and "off", etc.

from http://code.tutsplus.com/articles/number-systems-an-introduction-to-binary-hexadecimal-and-more--active-10848

     In converting binary to base 10 or decimal, you just need to follow the table above. You simply multiply the binary digit to its corresponding power of two value, depending on the position.

from http://drstienecker.com/tech-332/1-numbering-systems-and-conversions/

     The binary number 1101 (from the image above) yields a decimal equivalent of 13 (base 10).

Octal Number System

     Octal, or base 8, is composed of 0, 1, 2, 3, 4, 5, 6, and 7. It is like counting like the decimal way, but instead of 9, we end at 7.

from http://drstienecker.com/tech-332/1-numbering-systems-and-conversions/

     If in binary, we follow the power of two value, in octal we follow the power of eight in converting. The number 437 base 8 is equal to 287 base 10. How did we get that? Let's start with the ones place. 7 multiplied to 8 raised to 0 = 7x1 = 7. Tens place: 3 multiplied to 8 raised to 1 = 3x8 = 24. Hundreds place: 4 multiplied to 8 raised to 2 = 4x64 = 256. Adding them all up, we get 287. Simple, right?

Hexadecimal Number System (Base 16)

     Remember the colors when viewed in html? Those have digits composed of numbers 0-9 and letters A-F.

from Wikipedia (Web Colors)

     These digits are in hexadecimal. Hexadecimal, or base 16, is composed of 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F. A represents 10 in decimal, B is 11, C is 12, D is 13, E is 14, and F is 15.

from http://drstienecker.com/tech-332/1-numbering-systems-and-conversions/

     In converting hexadecimal to decimal, we follow the same pattern we use in binary and octal. The only difference is we use the power of 16 values as multiplier to the digits given.

     There are different converter apps out there in the internet, but it is still useful and liberating if we know these ourselves.

For more information, and conversion techniques (those that I did not explain further, like converting octal to binary, etc.), visit

1. http://code.tutsplus.com/articles/number-systems-an-introduction-to-binary-hexadecimal-and-more--active-10848 ; and

2. http://drstienecker.com/tech-332/1-numbering-systems-and-conversions/ .