Chapter 1: Data Storage

1. Chapter 1:Data Storage

2. Chapter 1: Data Storage • 1.1 Bits and Their Storage • 1.2 Main Memory • 1.3 Mass Storage • 1.4 Representing Information as Bit Patterns • 1.5 The Binary System

3. Chapter 1: Data Storage (continued) • 1.6 Storing Integers • 1.7 Storing Fractions • 1.8 Data and Programming • 1.9 Data Compression • 1.10 Communications Errors

4. Bits and Bit Patterns • Bit:Binary Digit (0 or 1) • Bit Patterns are used to represent information • Numbers • Text characters • Images • Sound • And others

5. Boolean Operations • Boolean Operation: An operation that manipulates one or more true/false values • Specific operations • AND • OR • XOR (exclusive or) • NOT

6. Boolean Operations • Boolean Operation: An operation that manipulates one or more true/false values • Specific operations • NAND • NOR • XNOR (exclusive NOR)

7. Figure 1.1 The possible input and output values of Boolean operations AND, OR, and XOR (exclusive or)

8. The possible input and output values of Boolean operations AND, OR, NAND and NOR (exclusive or)

9. The possible input and output values of Boolean operations AND, OR, NAND and NOR (exclusive or)

10. Gates • Gate: A device that computes a Boolean operation • Often implemented as (small) electronic circuits • Provide the building blocks from which computers are constructed • VLSI (Very Large Scale Integration)

11. Figure 1.2 A pictorial representation of AND, OR, XOR, and NOT gates as well as their input and output values

12. The possible input and output values of Boolean operations AND, OR, NAND and NOR (exclusive or)

13. The possible input and output values of Boolean operations AND, OR, NAND and NOR (exclusive or)

14. The possible input and output values of Boolean operations AND, OR, NAND and NOR (exclusive or)

15. The possible input and output values of Boolean operations AND, OR, NAND and NOR (exclusive or)

16. The possible input and output values of Boolean operations AND, OR, NAND and NOR (exclusive or)

17. The possible input and output values of Boolean operations AND, OR, NAND and NOR (exclusive or)

18. The possible input and output values of Boolean operations AND, OR, NAND and NOR (exclusive or)

19. Flip-flops Flip-flop: • A circuit built from gates that can store one bit (store information). • One input line is used to set its stored value to 1 • One input line is used to set its stored value to 0 • While both input lines are 0, the most recently stored value is preserved (remember information) • They're the kind of circuits that are used in computers to store program information - RAM memory

20. Figure 1.3 A simple flip-flop circuit

21. Figure 1.4 Setting the output of a flip-flop to 1

22. Figure 1.4 Setting the output of a flip-flop to 1 (continued)

23. Figure 1.4 Setting the output of a flip-flop to 1 (continued)

24. Figure 1.5 Another way of constructing a flip-flop

25. The Number System Integers can be written using a positional number system, in which each digit represents the coefficient in a power series N = an-1 rn-1 + an-2 rn-2 + an-3 rn-3 + … + a2 r2 + a1 r1 + a0r0 = an-1 rn-1 + an-2 rn-2 + an-3 rn-3 + … + a2 r2 + a1 r1 + a0 where n is the number of digits, r is the radix or base, and the ai are the coefficients, where each is an integer in the range 0 ≤ ai < r For decimal, r = 10, and the a’s are in the range 0 to 9. For the binary, r = 2, and the a’s are all either 0 or 1. For the hexadecimal, r = 16, the a’s are in the range 0 to 9, A, B, C, D, E, F.

26. The Number System The traditional decimal system is based on powers of ten. • Decimal Digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 The Binary system is based on powers of two. • Binary Digits : 0, 1 • The Octal system is based on powers of eight. • Octal digits: 0, 1, 2, 3, 4, 5, 6, 7 The Hexadecimal system is based on powers of sixteen. • Hexadecimal Digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, E, D, F

27. The Number Systems The traditional decimal system is based on powers of ten. 6237310 = 6*104 + 2*103 +3*102 +7*101 +3*100 The Binary system is based on powers of two. 11110011101001012 = 1*215 + 1*214 +1*213 +1*212 + 0*211 +0*210 +1*29 + 1*28 +1*27 +0*26 + 1*25 +0*24 +0*23+ 1*22 +0*21 +1*20 The Hexadecimal system is based on powers of sixteen. F3A516 = 15*163 + 3*162 +10*161 +5*160

28. Figure 1.7 The organization of a byte-size memory cell Address 0000 0000 0000 0004 0000 0008 0000 000C 0000 0010 0000 0014 0000 0018 0000 001C 0000 0020 0000 0024 0000 0028 0000 002C 0000 0030

29. Consider 8 binary digits to be one bytes Binary digits notation : 0, 1 Unsigned number: 101000112 = 1*27+ 0*26 +1*25 + 0*24+ 0*23 +0*22 +1*21 +1*20 = 128+32+2+1 = 16310

30. Figure 1.7 The organization of a byte-size memory cell Address 0000 0000 0000 0004 0000 0008 0000 000C 0000 0010 0000 0014 0000 0018 0000 001C 0000 0020 0000 0024 0000 0028 0000 002C 0000 0030 It requires 4 bytes to address 1 through 4 gigabytes the memory cells in the storage.

31. Octal decimal Notation • Octal decimal notation: A shorthand notation for long bit patterns • Divides a pattern into groups of three bits each • Represents each group by a single symbol • Example: 10100011 becomes 2438 10 100 011 = 010 100 011 = 243 010 = 0*22 +1*21 +0*20 = 2 100 = 1*22 +0*21 +0*20 = 4 011 = 0*22 +1*21 +1*20 = 3

32. Octal decimal Notation

33. Hexadecimal Notation • Hexadecimal notation: A shorthand notation for long bit patterns • Divides a pattern into groups of four bits each • Represents each group by a single symbol • Example: 10100011 becomes A3 1010 0011 1010 = 1*23+ 0*22 +1*21 +0*20 = 10 = A 0011 = 0*23+ 0*22 +1*21 +1*20 = 3

34. Figure 1.6 The hexadecimal coding system

35. The Number Systems The traditional decimal system is based on powers of ten. 6237310 = 6*104 + 2*103 +3*102 +7*101 +3*100 The Binary system is based on powers of two. 11110011101001012 = 1*215 + 1*214 +1*213 +1*212 + 0*211 +0*210 +1*29 + 1*28 +1*27 +0*26 + 1*25 +0*24 +0*23+ 1*22 +0*21 +1*20 The Hexadecimal system is based on powers of sixteen. F3A516 = 15*163 + 3*162 +10*161 +5*160

36. Conversion of Decimal to Binary 6237310 = 11110011101001012

37. Conversion of Binary to Decimal 11110011101001012 = 1*215 + 1*214 +1*213 +1*212 + 0*211 +0*210 +1*29 + 1*28 +1*27 +0*26 + 1*25 +0*24 + 0*23+ 1*22 +0*21 +1*20 =32768 + 16384 + 8192 + 4096 +512 + 256 +128 +32 +4 +1 = 6237310

38. Conversion of Binary to Hexadecimal 11110011101001012 = F3A5 1111 0011 1010 0101 1111 = 1*23+ 1*22 +1*21 +1*20 = 15 = F 0011 = 0*23+ 0*22 +1*21 +1*20 = 3 1010 = 1*23+ 0*22 +1*21 +0*20 = 10 = A 0101 = 0*23+ 1*22 +0*21 +1*20 = 5

39. Conversion of Decimal to Hexadecimal • 6237310 = F3A5 • Two ways: • Convert a decimal number to an equivalent binary number, which then convert to an equivalent hexadecimal number. • Example: 6237310 = 11110011101001012 • = F3A5

40. Conversion of Decimal to Hexadecimal • 6237310 = F3A5 • Two ways: • Convert a decimal number to an equivalent • hexadecimal number, using 16 as the advisor.

41. Main Memory Cells • Cell: A unit of main memory (typically 8 bits which is one byte) • Most significant bit: the bit at the left (high-order) end of the conceptual row of bits in a memory cell • Least significant bit: the bit at the right (low-order) end of the conceptual row of bits in a memory cell

42. Figure 1.7 The organization of a byte-size memory cell

43. Main Memory Addresses • Address: A “name” that uniquely identifies one cell in the computer’s main memory • The names are actually numbers. • These numbers are assigned consecutively starting at zero. • Numbering the cells in this manner associates an order with the memory cells.

44. Figure 1.8 Memory cells arranged by address

45. Memory Terminology • Random Access Memory (RAM): • Memory in which individual cells can be easily accessed in any order • a type of computer memory that can be accessed randomly; that is, any byte of memory can be accessed without touching the preceding bytes. • RAM composed of volatile memory • Types of RAM: There are two different types of RAM: • DRAM (Dynamic Random Access Memory) • SRAM (Static Random Access Memory).

46. Memory Terminology • Random Access Memory (RAM): • RAM composed of volatile memory • Types of RAM: There are two different types of RAM: • DRAM (Dynamic Random Access Memory) • SRAM (Static Random Access Memory). • They are volatile memory • The term dynamic indicates that the memory must be constantly refreshed (reenergized) or it will lose its contents. • RAM is sometimes referred to as DRAM (pronounced dee-ram) to distinguish it from static RAM (SRAM). • Static RAM is faster and less volatile than dynamic RAM, but it requires more power and is more expensive.

47. Memory Terminology • Read-only memory (ROM): • computer memory on which data has been prerecorded. • Once data has been written onto a ROM chip, it cannot be removed and can only be read. • Unlike main memory (RAM), ROM retains its contents even when the computer is turned off. • ROM is referred to as being nonvolatile, whereas RAM is volatile. • Erasable Read-only Memory (EPROM)

48. Memory Terminology • PROM (programmable read-only memory) • A memorychip on which data can be written only once. • Once a program has been written onto a PROM, it remains there forever. • Unlike RAM, PROMs retain their contents when the computer is turned off. • That is, PROM is non-volatile! • …

49. Memory Terminology • PROM (programmable read-only memory) • A memorychip on which data can be written only once. • PROM is non-volatile • The difference between a PROM and a ROM (read-only memory) is that • a PROM is manufactured as blank memory, • a ROM is programmed during the manufacturing process. • ….

50. Memory Terminology • PROM (programmable read-only memory) • A memorychip on which data can be written only once. • PROM is non-volatile • PROM is manufactured as blank memory • a PROM is manufactured as blank memory, whereas • a ROM is programmed during the manufacturing process. • To write data onto a PROM chip, a special device called a PROM programmer or PROM burner is needed. The process of programming a PROM is sometimes called burning the PROM.