1. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Complex Combinational Logic Blocks ECE/CS 252, Fall 2010 Prof. Mikko Lipasti Department of Electrical and Computer Engineering University of Wisconsin – Madison

2. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 3-2 Building Functions from Logic Gates We've already seen how to implement truth tables using AND, OR, and NOT -- an example of combinational logic. Combinational Logic Circuit output depends only on the current inputs Stateless Quick review + example Then examples of some useful combinational circuits

3. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 3-3 Review: Building AND/OR/NOT Logic Circuit Can implement ANY truth table with AND, OR, NOT. ABCD 0000 0010 0101 0110 1000 1011 1100 1110 1. AND combinations that yield a "1" in the truth table. 2. OR the results of the AND gates.

4. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 3-4 Decoder n inputs, 2 n outputs exactly one output is 1 for each possible input pattern 2-bit decoder

5. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Example: 7-Segment Display Decoder 3-5 ABCDs1s2s3s4s5s6s7 00001110111 00010010010 00101011101 00111011011 01000111010 01011101011 01101101111 01111010010 10001111111 10011111011 s2 s5 s1 s3 s6 s7 s4 4:16 Decoder A B C D 0000 0001 0010 0011 0100 0101 0110 0111 1000 1001 1010 1011 1100 1101 1110 1111 s5

6. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 3-6 Full Adder Add two bits and carry-in, produce one-bit sum and carry-out. ABC in SC out 00000 00110 01010 01101 10010 10101 11001 11111

7. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 3-7 Four-bit Ripple-Carry Adder

8. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 3-8 Multiplexer (MUX) n-bit selector and 2 n inputs, one output output equals one of the inputs, depending on selector 4-to-1 MUX

9. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. LC-3 Arithmetic/Logic Unit (ALU) 3-9 16-bit Adder16-bit AND16-bit NOT Left OperandRight Operand Result Mux ctrl: 00 – Add 01 – AND 10 – NOT 11 – N/A

10. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 3-10 Summary Building AND/OR/NOT Logic Functions Useful Complex Logic Blocks Decoder Full Adder Ripple-carry Adder Multiplexer LC-3 Arithmetic-Logic Unit (ALU)