1. 1 Digital Logic Design Engr. Kashif Shahzad

2. 2 What’s Course About?  Digital logic, focusing on the design of computers  Stay above transistor level Only one class on transistors and VLSI Only one class on transistors and VLSI  Each person designs a MIPS CPU and peripheral logic (VGA, joystick) and peripheral logic (VGA, joystick) Project like an Atari 2600 game Project like an Atari 2600 game  High-level language Modern design practices Modern design practices

3. 3 How Can We Do This?  Field Programmable Gate Arrays Chips with a lot of circuits Chips with a lot of circuits  Tens of thousands to millions of transistors Programmable Programmable  We write “programs” describing design  Tools translate to gates/wires  Download pattern to chip

4. 4 Use This Board

5. 5 Schematic Diagram

6. 6Verilog/* * A 32-bit counter with only 4 bits of output. The idea is * A 32-bit counter with only 4 bits of output. The idea is * to select which of the counter stages you want to pass on. * to select which of the counter stages you want to pass on. * * Anselmo Lastra, November 2002 * Anselmo Lastra, November 2002 */ */ module cntr_32c(clk,res,out); module cntr_32c(clk,res,out); input clk; input clk; input res; input res; output [3:0] out; output [3:0] out; reg [31:0] count; reg [31:0] count; always @ (posedge res or posedge clk) if(res) if(res) count <= 0; else count <= count + 1; count <= count + 1; assign out[3] = count[28]; assign out[3] = count[28]; assign out[2] = count[27]; assign out[2] = count[27]; assign out[1] = count[26]; assign out[1] = count[26]; assign out[0] = count[25]; assign out[0] = count[25];endmodule

7. 7 Binary Signaling  Zero volts FALSE or 0 FALSE or 0  3.3 or 5 volts TRUE or 1 TRUE or 1  Modern chips down to 1V  Why not multilevel signaling?

8. 8 Discrete Data  Some data inherently discrete Names (sets of letters) Names (sets of letters)  Some quantized Music recorded from microphone Music recorded from microphone Note that other examples like music from CD or electronic keyboard already quantized Note that other examples like music from CD or electronic keyboard already quantized Mouse movement is quantized Mouse movement is quantized  Well, some mice

9. 9BCD  Binary Coded Decimal  Decimal digits stored in binary Four bits/digit Four bits/digit Like hex, except stops at 9 Like hex, except stops at 9 Example Example 931 is coded as 1001 0011 0001 931 is coded as 1001 0011 0001  Remember: these are just encodings. Meanings are assigned by us.

10. 10 Other Codes Exist  Non positional  Example: Gray Code Only one bit changes at a time Only one bit changes at a time 000,001,011,010,110,111,101,100 000,001,011,010,110,111,101,100 Why is this useful? Why is this useful? Actually there’s a family of Gray codes Actually there’s a family of Gray codes Ref: http://lib-www.lanl.gov/numerical/bookcpdf/c20-2.pdf

11. 11 Shaft Encoder

12. 12 Character Codes  From numbers to letters  ASCII Stands for American Standard Code for Information Interchange Stands for American Standard Code for Information Interchange Only 7 bits defined Only 7 bits defined  Unicode  You may make up your own code for the MIPS VGA

13. 13 ASCII table

14. 14 Even Parity  Sometimes high-order bit of ASCII coded to enable detection of errors  Even parity – set bit to make number of 1’s even  Examples A (01000001) with even parity is 01000001 C (01000011) with even parity is 11000011

15. 15 Odd Parity  Similar except make the number of 1’s odd  Examples A (01000001) with odd parity is 11000001 C (01000011) with odd parity is 01000011

16. 16 Error Detection  Note that parity detects only simple errors One, three, etc. bits One, three, etc. bits  More complex methods exist  Some that enable recovery of original info Cost is more redundant bits Cost is more redundant bits

17. 17 Today’s Topics  Introduction  Digital logic  Number systems  Arithmetic  Codes  Parity  The encoding is key Standards are used to agree on encodings Standards are used to agree on encodings Special purpose codes for particular uses Special purpose codes for particular uses

18. 18Homework  None, but…  I expect you to know number systems well and be able to do conversions and arithmetic Decimal – Binary Decimal – Binary Binary – Decimal Binary – Decimal Decimal – Hex Decimal – Hex Hex – Decimal Hex – Decimal  Can do some of the problems – 1-2, 1-4, 1-7 if you think you need a refresher. Answers on book website.

19. 19 Binary – Powers of 2  Positional representation  Each digit represents a power of 2 So 101 binary is 1 2 2 + 0 2 1 + 1 2 0 1 2 2 + 0 2 1 + 1 2 0or 1 4 + 0 2 + 1 1 = 5 1 4 + 0 2 + 1 1 = 5

20. 20 Converting Binary to Decimal  Easy, just multiply digit by power of 2  Just like a decimal number is represented  Example follows

21. 21 Binary  Decimal Example 76543210 27272727 26262626 25252525 24242424 23232323 22222222 21212121 20202020 1286432168421 10011100 128 + 0 + 0 + 16 + 8 + 4 + 0 + 0 = 156 What is 10011100 in decimal?

22. 22 Decimal to Binary  A little more work than binary to decimal  Some examples 3 = 2 + 1 = 11 (that’s 12 1 + 12 0 ) 3 = 2 + 1 = 11 (that’s 12 1 + 12 0 ) 5 = 4 + 1 = 101 (that’s 12 2 + 02 1 + 12 0 ) 5 = 4 + 1 = 101 (that’s 12 2 + 02 1 + 12 0 )

23. 23 Algorithm – Decimal to Binary  Find largest power-of-two smaller than decimal number  Make the appropriate binary digit a ‘1’  Subtract the power of 2 from decimal  Do the same thing again

24. 24 Decimal  Binary Example  Convert 28 decimal to binary 76543210 27272727 26262626 25252525 24242424 23232323 22222222 21212121 20202020 1286432168421 32 is too large, so use 16 Binary  10000Decimal  28 – 16 = 12 Binary  11000Decimal  12 – 8 = 4 Next is 8 Binary  11100Decimal  4 – 4 = 0 Next is 4

25. 25Hexadecimal  Strings of 0s and 1s too hard to write  Use base-16 or hexadecimal – 4 bits DecBinHex 000000 100011 200102 300113 401004 501015 601106 701117DecBinHex810008 910019 101010? 111011? 121100? 131101? 141110? 151111?

26. 26Hexadecimal  Letters to represent 10-15 DecBinHex 000000 100011 200102 300113 401004 501015 601106 701117DecBinHex810008 910019 101010a 111011b 121100c 131101d 141110e 151111f Power of 2Power of 2 Size of byteSize of byte Why use base 16?

27. 27 Hex to Binary  Convention – write 0x before number  Hex to Binary – just convert digits BinHex 00000 00011 00102 00113 01004 01015 01106 01117 10008 10019 1010a 1011b 1100c 1101d 1110e 1111f 0x2ac 001010101100 0x2ac = 001010101100 No magic – remember hex digit = 4 bits

28. 28 Binary to Hex  Just convert groups of 4 bits BinHex 00000 00011 00102 00113 01004 01015 01106 01117 10008 10019 1010a 1011b 1100c 1101d 1110e 1111f 101001101111011 1011 537b 101001101111011 = 0x537b 0101  0111  0011 

29. 29 Hex to Decimal  Just multiply each hex digit by decimal value, and add the results.  16 3 16 2 16 1 16 0 4096256161 0x2ac 2 256 + 10 16 + 12 1 = 684 DecHex00 11 22 33 44 55 66 77 88 99 10a 11b 12c 13d 14e 15f

30. 30 Decimal to Hex Analogous to decimal  binary. 1. Find largest power-of-16 smaller than decimal number 2. Divide by power-of-16. The integer result is hex digit. 3. The remainder is new decimal number. 4. Do the same thing again

31. 31 Decimal to Hex  16 3 16 2 16 1 16 0 4096256161 DecHex00 11 22 33 44 55 66 77 88 99 10a 11b 12c 13d 14e 15f 684 684/256 = 2 0x2__ 684%256 = 172 172/16 = 10 = a 0x2a_ 172%16 = 12 = c 0x2ac

32. 32Octal  Octal is base 8  Similar to hexadecimal Conversions Conversions  Less convenient for use with 8-bit bytes

33. 33 Arithmetic -- addition  Binary similar to decimal arithmetic 01100 +10001 11101 No carries10110010110 +10111 101101 Carries 1+1 is 2 (or 10 2 ), which results in a carry

34. 34 Arithmetic -- subtraction 10110 -10010 00100 No borrows0011011110 -10011 01011 Borrows 0 - 1 results in a borrow

35. 35 Arithmetic -- multiplication 1011 0000 1011 110111 Successive additions of multiplicand or zero, multiplied by 2 (10 2 ). Note that multiplication by 10 2 just shifts bits left. 1011X 101

36. 36 Hexadecimal Arithmetic  Similar  If you’re doing by hand, easiest to convert each set of digits to decimal and back  Skill is not very useful…