1. Digital Computers and Information Chapter 1 Mano and Kime

2. Digital Computers and Information Digital Computers Number Systems Arithmetic Operations Decimal Codes Error Detection and Correction

3. Block Diagram of Computer

4. Memory ROMs and PROMs EPROMs, EEPROMs and Flash Memory Static RAMs and Dynamic RAMs

5. ROMs and PROMs ROM –Read-Only Memory PROM –Programmable Read-Only Memory

6. EPROMs, EEPROMs and Flash Memory EPROM –Erasable Programmable Read-Only Memory –Erase with ultraviolet light EEPROM –Electrically-Erasable Programmable Read-Only Memory Flash Memory –Electrically-Erasable in bulk

7. RAMs RAM –Random-Access Memory –Read-Write Memory Static RAM –Needs 4 transistors per bit to make a latch –Data lost when power is turned off Dynamic RAM –One transistor per bit –Data stored as charge on a capacitor –Data must be continually refreshed

8. W8X Microcontroller Control Unit Datapath

9. The W8Z Microprocessor

10. Digital Computer and Information Digital Computers Number Systems Arithmetic Operations Decimal Codes Error Detection and Correction

11. Powers of 2

12. Numbers with Different Bases

13. Number Systems N =...P 3 P 2 P 1 P 0. P -1 P -2 P -3... =... + P 3 b 3 + P 2 b 2 + P 1 b 1 + P 0 b 0 + P -1 b -1 + P -2 b -2 + P -3 b -3 +... 375.17 10 = 3 x 10 2 + 7 x 10 1 + 5 x 10 0 + 1 x 10 -1 + 7 x 10 -2 = 300 + 70 + 5 + 0.1 + 0.07 = 375.17

14. Number Systems N =...P 3 P 2 P 1 P 0. P -1 P -2 P -3... =... + P 3 b 3 + P 2 b 2 + P 1 b 1 + P 0 b 0 + P -1 b -1 + P -2 b -2 + P -3 b -3 +... 1101.11 2 = 1 x 2 3 + 1 x 2 2 + 0 x 2 1 + 1 x 2 0 + 1 x 2 -1 + 1 x 2 -2 = 8 + 4 + 0 + 1 + 1/2 + 1/4 = 13.75 10 Binary

15. Number Systems N =...P 3 P 2 P 1 P 0. P -1 P -2 P -3... =... + P 3 b 3 + P 2 b 2 + P 1 b 1 + P 0 b 0 + P -1 b -1 + P -2 b -2 + P -3 b -3 +... 1AB.6 16 = 1 x 16 2 + A x 16 1 + B x 16 0 + 6 x 16 -1 = 1 x 256 + 10 x 16 + 11 x 1 + 6/16 = 256 + 160 + 11 + 0.375 = 427.375 10 Hex

16. Number Systems N =...P 3 P 2 P 1 P 0. P -1 P -2 P -3... =... + P 3 b 3 + P 2 b 2 + P 1 b 1 + P 0 b 0 + P -1 b -1 + P -2 b -2 + P -3 b -3 +... 173.25 8 = 1 x 8 2 + 7 x 8 1 + 3 x 8 0 + 2 x 8 -1 + 5 x 8 -2 = 1 x 64 + 7 x 8 + 3 x 1 + 2/8 + 5/64 = 64 + 56 + 3 + 0.25 + 0.078125 = 123.328125 10 Octal

17. Examples Convert the following binary numbers to decimal: 1101001 10001011.011 10011010

18. Digital Computer and Information Digital Computers Number Systems Arithmetic Operations Decimal Codes Error Detection and Correction

19. Recall Full Adder Truth Table 0 0 0 0 0 0 0 1 1 0 0 1 0 1 0 0 1 1 0 1 1 0 0 1 0 1 0 1 0 1 1 1 0 0 1 1 1 1 1 1 C i A i B i S i C i+1 0 0 1 0 1 1 1 A B 0 1 0 1 1 1 1 C Final carry = 0

20. Binary Addition 0 0 1 1 0 1 0 1 0 0 0 1 1 0 0 1 0111 0 0 1 0 53 +25 78 35 +19 4E Dec Hex Binary 1 001 1 0 0

21. Number System Conversions Hex, Binary, and Octal to Decimal Binary Hex Binary Octal Hex Octal Decimal to Hex, Octal, and Binary

22. Hex to Decimal 87C987C9 x 16 128 + 7 135 x 16 2,160 + 12 2,172 x 16 34,752 + 9 34,761

23. Binary Hex 0110 1010 1000. 1111 0101 1100 6A8. F 5 C

24. Binary Octal 011 010 101 000. 111 101 011 100 3 2 5 0. 7 5 3 4

25. Hex Octal Go through Binary 0110 1010 1000. 1111 0101 1100 6A8. F 5 C 011 010 101 000. 111 101 011 100 3 2 5 0. 7 5 3 4

26. Convert Decimal to any Base Integer Part: Divide by the base, keep track of the remainder, and read up. 16 34,761 16 2,172rem 9 16 135 rem 12 = C 16 8 rem 7 0 rem 8 Read up 34,761 10 = 87C9 16

27. Convert Decimal to any Base Fractional Part: Multiply by the base, keep track of the integer part, and read down. 0.78125 x 16 = 12.5 int = 12 = C 0.5 x 16 = 8.0 int = 8 Read down 0.78125 10 = 0.C8 16

28. Convert Decimal to any Base Fractional Part: Multiply by the base, keep track of the integer part, and read down. 0.1 x 2 = 0.2 int = 0 0.2 x 2 = 0.4 int = 0 0.4 x 2 = 0.8 int = 0 0.8 x 2 = 1.6 int = 1 0.6 x 2 = 1.2 int = 1 0.2 x 2 = 0.4 int = 0 0.4 x 2 = 0.8 int = 0 Read down 0.1 10 = 0.00011 2

29. Examples Convert the following numbers from the given base to the other three bases listed in the table: DecimalBinaryOctalHex 369.3125??? ?10111101.101?? ??326.5? ???F3C7.A

30. Binary Coded Decimal Code decimal numbers using the binary digits, 0 - 9. That is, 0000 - 1001. Can NOT use the hex digits A - F. For example, the DECIMAL number 3582 would be coded in BCD as 0011 0101 1000 0010 While this looks like the HEX number 3582H in BCD we interpret it as the DECIMAL number 3582.

31. BCD Addition Binary 35H 00110101 +47H 01000111 7CH 01111100 Decimal (BCD) 35H 00110101 +47H 01000111 82H 10000010 0000 B0 35 MOV AL,35H ;AL = 35H 0002 04 47 ADD AL,47H ;AL = AL+47H 0004 27 DAA ;Decimal adjust

32. Digital Computer and Information Digital Computers Number Systems Arithmetic Operations Decimal Codes Error Detection and Correction

33. Use of Parity Bit - Extra bit included to make the total number of 1’s either even or odd. Refer to page : 22 for an example. * If a parity error is detected at the receiving end, it can request for a retransmission.

34. More topics… Fixed and Floating point numbers – Refer to the ppt presentation on the course website.