This preview shows pages 1–9. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Numbering Systems Math and Conversion Decimal Octal Hexadecimal Binary Conversion When does When does 5 5 * * 8 = 8 = Or Or 0101 0101 * * 1000 = 1000 = 50 50 28 28 40 40 101000 101000 Decimal system the decimal number system we use every day is built on base ten it is based on 10 positions numbered 0 thru 9 each position corresponds to a power of 10 1024 is: 1 x 1000 = 1000 0 x 100 = 000 2 x 10 = 20 4 x 1 = 4 Decimal Numbers The easiest way to understand bits is to compare them to something you know: digits A digit is a single place that can hold numerical values between 0 and 9. Digits are normally combined together in groups to create larger numbers. For example, 6,357 has four digits. It is understood that in the number 6,357, the 7 is filling the "1s place," while the 5 is filling the 10s place, the 3 is filling the 100s place and the 6 is filling the 1,000s place. So you could express things this way if you wanted to be explicit: (6 * 1000) + (3 * 100) + (5 * 10) + (7 * 1) = 6000 + 300 + 50 + 7 = 6357 powers of 10. Assuming that we are going to represent the concept of "raised to the power of" with the "^" symbol (so "10 squared" is written as "10^2"), another way to express it is like this: (6 * 10^3) + (3 * 10^2) + (5 * 10^1) + (7 * 10^0) = 6000 + 300 + 50 + 7 = 6357 Binary system computer memory is based on the electrical representation of data each memory position is represented by a bit which can be either 'on' or 'off'. This makes it easier to represent computer memory using a base 2 number system rather than the base 10 decimal system. Binary system represents numbers by a series of 1's and 0's. a 1 represents an 'on' position a 0, an 'off' position a hex byte is represented by 8 bits numbered 0 to 7 from left to right the leftmost bit is called the highorder bit, the right most bit, the low order bit. Bytes (Hexadecimal) Bits are rarely seen alone in computers. They are almost always bundled together into 8bit collections, and these collections are called bytes. Why are there 8 bits in a byte? The 8bit byte is the MOST efficient way to use memory each bit in a byte (2 hexadecimal characters) is used. With 8 bits in a byte, you can represent 256 values ranging from 0 to 255, as shown here: 0 = 00000000 1 = 00000001 2 = 00000010 .. 254 = 11111110 255 = 11111111 BINARY uses base 2 Each binary digit is represented by 1 bit An binary byte equals 1 bit Binary digits are represented by 0 thru 1 each position is a power of 2 used inside the computer and expressed as ON or OFF Octal uses base 8 Each octal digit is represented by 3 bits An octal byte equals 6 bits octal digits are represented by 0 thru 7 each position is a power of 8 Rarely seen today only used for specific purposes ( network addressing, permissions in Unix, ,,,,) Hexadecimal...
View
Full
Document
This note was uploaded on 02/19/2012 for the course HWD 101 taught by Professor Brain during the Spring '11 term at Seneca.
 Spring '11
 brain

Click to edit the document details