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# Number systems

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### Number systems

1. 1. Computer language Everything that is stored and processed inside a computer (all data, information, instructions, files, images, etc.) is stored as numbers. More specifically, everything inside a computer is actually a Binary number (0 or 1) The CPU is made up of millions of tiny switches that can only be in one of the two states, either “ON” or “OFF”. While the processing data is taking place, the switches will alternate between these two states.
2. 2. Number Systems There are infinite ways to represent a number. Some of them associated with modern computers and digital electronics are: ● Decimal ● Binary ● Hexadecimal
3. 3. Decimal (base 10) It's the way most human beings represent numbers. ● Decimal counting goes: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, and so on.
4. 4. Binary (base 2) It's the natural way most digital circuits represent and manipulate numbers. ● Binary counting goes: 0, 1, 10, 11, 100, 101, 110, 111, 1000, 1001, 1010, 1011, 1100, 1101, 1110, 1111, 10000, 10001, and so on.
5. 5. Hexadecimal (base 16) It's currently the most popular choice for representing digital circuit numbers in a form that is more compact than binary. ● Hexadecimal counting goes: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F, 10, 11, and so on.
6. 6. Decimal number conversion A repeated division and remainder algorithm can convert decimal to binary or hexadecimal. ● Divide the decimal number by the desired target radix (2 or 16). ● Append the remainder as the next most significant digit. ● Repeat until the decimal number has reached zero.
7. 7. What is a bit? ● A bit is a Binary Digit (the word comes from Binary DigIT) ● A bit is the smallest unit of information that we can store on a computer (0 or 1).
8. 8. What is a Byte? ● Bits (b) are usually grouped into groups of 8, and each group is called a Byte. (10101011) ● Bytes (B) are the standard unit of storage for all computing devices. ● A single keyboard character that you type, such as letter “A” takes up one byte of storage.
9. 9. Storing data units UnitUnit Symbol Equivalent BYTE B 8 BITS KILOBYTE KB 1024 BYTES MEGABYTE MB 1024 KILOBYTES GIGABYTE GB 1024 MEGABYTES TERABYTE TB 1024 GIGABYTES
10. 10. ACTIVITIES 1. Convert 0110 binary to decimal 2. Convert 100011 binary to decimal 3. Convert 55 decimal to binary 4. Convert 205 decimal to binary 5. Which number is higher, 01001000 or 01000010. Why? Don't convert them to decimal. 6. In binary system, how many characteres can be represented with 3 digits? And with 8? Write the highest number that can be represented in both cases. 7. Convert 17F hexadecimal to decimal 8. Convert 1792 decimal to hexadecimal
11. 11. ACTIVITIES 9. Convert 111100 binary to hexadecimal 10. Convert 70 hexadecimal to binary 11. Which number is higher, 11100111 or E7? 12. How many bytes takes up your name and surname? 13. How many bits fits onto a 700 MB CD-ROM? 14. What is the size difference between the different storage devices in each of the pairs below? a) A 100 kB file and a 4,7 GB DVD b) A 500 GB external hard disk and a 700 MB CD-ROM c) A 4 GB memory stick and a 1 TB hard disk d) A 16 GB MP3 player and an old 1,44 MB floppy disc