1. CMSC 104 1 Machine Architecture and Number Systems Topics Major Computer Components Bits, Bytes, and Words The Decimal Number System The Binary Number System Converting from Binary to Decimal Converting from Decimal to Binary The Hexidecimal Number System

2. CMSC 104 2 Major Computer Components Central Processing Unit (CPU) Bus Main Memory (RAM) Secondary Storage Media I / O Devices

3. CMSC 104 3 The CPU Central Processing Unit The “brain” of the computer Controls all other computer functions In PCs (personal computers) also called the microprocessor or simply processor.

4. CMSC 104 4 The Bus Computer components (Such as: the CPU, Main Memory, & Hard Disks) are connected by a bus. A bus is a group of parallel wires that carry control signals and data between components.

5. CMSC 104 5 Main Memory Main memory holds information such as computer programs, numeric data, or a document created by a word processor. Main memory is made up of capacitors. If the capacitor is charged, then its state is said to be 1 or ON. We could also say the bit is set. If the capacitor does not have a charge, then its state is 0 or OFF. We could also say that the bit is reset or cleared. 0,1

6. CMSC 104 6 Main Memory (con’t) Memory is divided into cells, where each cell contains 8 bits (1’s or 0’s). Eight bits is called a byte. Each of these cells is numbered. The number associated with a cell is known as its address. Main memory is volatile storage. That is, if power is lost, the information in main memory is lost.

7. CMSC 104 7 Main Memory (con’t) In addition to the circuitry that holds the bits, there are other circuits that allow other components (Like the CPU) to: o get the information held at a particular address in memory, known as a READ, o or store information at a particular address in memory, known as a WRITE.

8. CMSC 104 8 Main Memory (con’t) All addresses in memory can be accessed in the same amount of time. We do not have to start at address 0 and read everything until we get to the address we really want. We can go directly to the address we want and access the data. That is why we call main memory RAM (Random Access Memory).

9. CMSC 104 9 Secondary Storage Media Disks -- floppy, hard, removable (random access) Tapes (sequential access) CDs (random access) DVDs (random access) Secondary storage media store files that contain o computer programs o data files o other types of information This type of storage is called persistent (permanent) storage because it is non-volatile.

10. CMSC 104 10 I/O (Input/Output) Devices Information input/output is handled by I/O (peripheral) devices. A peripheral device is a component that is not an integral part of the computer. Examples: o monitor o keyboard o mouse o disk drive (floppy, hard, removable) o CD or DVD drive o printer o scanner

11. CMSC 104 11 Computer/Peripheral Communication Ports o locations through which data can enter or leave the computer (plugs on back) o identified by port numbers like memory cells are identified by addresses

12. CMSC 104 12 Parallel and Serial Communication l Refer to the manner in which bit patterns are transferred with respect to time. l Parallel - All the bits of a pattern are transferred at the same time, with each bit being transferred on a separate line. Requires multi-wire cables. l Serial - Transmits one bit at a time. Slower, but uses a simpler data path.

13. CMSC 104 13 Bits, Bytes, and Words A bit is a single binary digit (a 1 or 0). A byte is 8 bits A word is 32 bits or 4 bytes (machine dependant) Long word = 8 bytes = 64 bits Quad word = 16 bytes = 128 bits Programming languages use these standard number of bits when organizing data storage and access. What do you call 4 bits ?? (hint: it is a small byte)

14. CMSC 104 14 From “C How to Program” 4 rd edition Deitel & Deitel, ISBN# = 0-13-142644-3 Items covered in the this part of class: Page 1206 - Number Systems: binary, decimal, hex Page 1209 - Number System Representations Page 1210 - Converting Binary to Decimal - Converting Decimal to Binary/Hex

15. CMSC 104 15 The Binary Number System The on and off states of the capacitors in RAM can be thought of as the values 1 and 0. Therefore, thinking about how information is stored in RAM requires knowledge of the binary (base 2) number system. Let’s review the decimal (base 10) number system first.

16. CMSC 104 16 The Decimal Number System The decimal number system is a positional number system. Example: 5 6 2 11 X 10 0 1000 100 10 1 2 X 10 1 6 X 10 2 5 X 10 3

17. CMSC 104 17 The Decimal Number System (con’t) The decimal number system is also known as base 10. The values of the positions are calculated by taking 10 to some power. Why is the base 10 for decimal numbers? o Because we use 10 digits, the digits 0 through 9.

18. CMSC 104 18 The Binary Number System The binary number system is called binary because it uses base 2. The values of the positions are calculated by taking 2 to some power. Why is the base 2 for binary numbers ? o Because we use 2 digits, the digits 0 and 1.

19. CMSC 104 19 The Binary Number System (con’t) The binary number system is also a positional numbering system. Instead of using ten digits, 0 - 9, the binary system uses only two digits, 0 and 1. Example of a binary number and the values of the positions: 1 0 0 0 0 0 1 2 6 2 5 2 4 2 3 2 2 2 1 2 0

20. CMSC 104 20 Converting from Binary to Decimal 1 0 0 0 0 0 1 1 X 2 0 = 1 2 6 2 5 2 4 2 3 2 2 2 1 2 0 0 X 2 1 = 0 0 X 2 2 = 0 2 0 = 1 2 4 = 16 0 X 2 3 = 0 2 1 = 2 2 5 = 32 0 X 2 4 = 0 2 2 = 4 2 6 = 64 0 X 2 5 = 0 2 3 = 81 X 2 6 = 64 65

21. CMSC 104 21 Converting from Binary to Decimal (con’t) Practice conversions: Binary Decimal 101011 1000001 111

22. CMSC 104 22 Converting Decimal to Binary l First make a list of the values of 2 to the powers of 0 to 8, then use the subtraction method. 2 0 = 1, 2 1 = 2, 2 2 = 4, 2 3 = 8, 2 4 = 16, 2 5 = 32, 2 6 = 64, 2 7 = 128, 2 8 = 256 l Example:4242 10 2 - 32 - 8 - 2 1 0 1 0 1 0 2 5 2 4 2 3 2 2 2 1 2 0

23. CMSC 104 23 Counting in Binary l Binary 0 1 10 11 100 101 110 111 l Decimal equivalent 0 1 2 3 4 5 6 7

24. CMSC 104 24 Addition of Binary Numbers l Examples: 1 0 0 10 0 0 11 1 0 0 + 0 1 1 0 + 1 0 0 1 + 0 1 0 1 1 1 1 11 0 1 0 1 0 0 0 1

25. CMSC 104 25 Addition of Large Binary Numbers l Example showing larger numbers: 1 0 1 0 0 0 1 1 1 0 1 1 0 0 0 1 + 0 1 1 1 0 1 0 0 0 0 0 1 1 0 0 1 1 0 0 0 1 0 1 1 1 1 1 0 0 1 0 1 0

26. CMSC 104 26 Working with Large Numbers 0 1 0 1 0 0 0 0 1 0 1 0 0 1 1 1 = ? Humans can’t work well with binary numbers; there are too many digits to deal with. Memory addresses and other data can be quite large. Therefore, we sometimes use the hexadecimal number system.

27. CMSC 104 27 Hexadecimal Binary 0 1 0 1 0 0 0 0 1 0 0 1 0 1 1 1 Hex 5 0 9 7 Written: 5097 16

28. CMSC 104 28 What is Hexadecimal really ? Binary 0 1 0 1 0 0 0 0 1 0 0 1 0 1 1 1 Hex 5 0 9 7 A number expressed in base 16. It’s easy to convert binary to hex and hex to binary because 16 is 2 4.

29. CMSC 104 29 Hexadecimal l Binary is base 2, because we use two digits, 0 and 1 l Decimal is base 10, because we use ten digits, 0 through 9. l Hexadecimal is base 16. How many digits do we need to express numbers in hex ? 16 (0 through ?) l 0 1 2 3 4 5 6 7 8 9 A B C D E F

30. CMSC 104 30 The Hexadecimal Number System (con’t) Binary Decimal Hexadecimal 0 0 0 1010 10 A 1 1 1 1011 11 B 10 2 2 1100 12 C 11 3 3 1101 13 D 100 4 4 1110 14 E 101 5 5 1111 15 F 110 6 6 111 7 7 1000 8 8 1001 9 9

31. CMSC 104 31 The Hexadecimal Number System (con’t) Example of a hexadecimal number and the values of the positions: 3 C 8 B 0 5 1 16 6 16 5 16 4 16 3 16 2 16 1 16 0

32. CMSC 104 32 Example of Equivalent Numbers Binary: 1 0 1 0 0 0 0 1 0 1 0 0 1 1 1 2 Decimal: 20647 10 Hexadecimal: 50A7 16 Notice how the number of digits gets smaller as the base increases.