Menu. 7-Segment LED. Misc. 7-Segment LED MSI Components >MUX >Adders Memory Devices >D-FF, RAM, ROM Computer/Microprocessor >GCPU

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1 Menu 7-Segment LED MSI Components >MUX >Adders Memory Devices >D-FF, RAM, ROM Computer/Microprocessor >GCPU Look into my Segment LED a b c h GND c g b d f a e h Show 7-segment LED in LogicWorks, 7-Segment Display * See also the LogicWorks 4-output device called Hex Keyboard See also the LogicWorks 4-input device called Hex Display abc defg A = abc defg F = University of Florida, File 04 1

2 Multiplexer (MUX) MUX: Multiplexer/Data Selector X 0 (H) X 1 (H) X 2 (H) X 3 (H) I 0 I 1 I 2 I 3 4-input MUX S 1 S 0 Z(H) Z = X (S1,S 0) 2 Thus, if S 1 S 0 = 10 2, then Z = X 2 S 1 (H) S 0 (H) X 0 X 1 X 2 X 3 S 1 S 0 Z A MUX switches a choice of any single input to a single output 3 Multiplexer (MUX) Equation I 0 I 1 4-input Z S 1 S 0 I 3 I 2 I 1 I 0 Z I 2 MUX I 3 S 1 S We call this a 4-input MUX (even though there are 6 inputs). Since 6 inputs, would be 2 6 = 64 rows in a truth table Use wild cards (- or *) for inputs that can take on both values Z = /S 1 /S 0 I 0 + /S 1 S 0 I 1 + S 1 /S 0 I 2 + S 1 S 0 I 3 4 University of Florida, File 04 2

3 Binary Adder Suppose we want to add two 2-bit numbers Carry Sum = /X Y + X /Y = X Y Carry = X Y 5 Notation for Binary Addition For the circuit with no carry in, we implement as follows: x i s y i i s i = x i y i c i+1 = x i y i This circuit is called a Half-Adder Notation: A 4-bit number is represented by b 3 b 2 b 1 b 0. Thus, we get bits b 0 ~b N-1 where N = # of bits. If we add two 4-bit numbers, must we add 3 # s, not 2 # s c 3 c 2 c 1 c 0 = 0 c i = carry bit x 3 x 2 x 1 x 0 x i = 1 st number y 3 y 2 y 1 y 0 y i = 2 nd number c 4 s 3 s 2 s 1 s 0 s i = sum c i+1 6 University of Florida, File 04 3

4 Adder with Carry Input Let us include a carry input (c in ) in the design: Sum = /x*/y* c in + /x* y*/c in + x*/y*/c in + x* y* c in With a little bit of algebra, we can derive: Sum = x y c in 7 Carry Out of Full Adder Sum of all possible pairs XOR of all inputs Sum=x y c in c out = x y + x c in + y c in Q: Is the order important? Q: Why? x y c inx y x c in y c in Sum = s i c in = c i & c out = c i+1 Sum c out x i y i c i This circuit is called a Full-Adder s FA c o s i c i+1 8 University of Florida, File 04 4

5 Y 3 X 3 C 3 Ripple-Carry Adders Thus, to add two 4-bit numbers we need 4 Full- Adders as follows: Y 2 X 2 C 2 Y 1 X 1 C 1 Y 0 X 0 C 0 =0 FA 0 (C 0 =0) FA 3 FA 2 FA OR 1 HA (no C 0 ) C 4 S 3 C 3 S 2 C 2 S 1 C 1 S 0 Actually, we could replace FA 0 with a half-adder is a 4-bit look-ahead carry adder 9 ALU (74 181) ALU: Arithmetic Logic Unit Lam Fig University of Florida, File 04 5

6 D-FF: Delay, Data Flip-Flop Memory Devices > Rising edge-triggered shown to right > Falling-edge Q D triggered here /Q RAM: Random Access Memory ROM: Read Only Memory 13 A 12-0 ROM CS/CE D D A 9 ~ A 0 D 7 ~ D 0 RAM CS/CE WE Q /Q 11 Computer Functional Block Diagram I/O ALU MEMORY CONTROL CPU DATA CONTROL ADDRESS bus not shown 12 University of Florida, File 04 6

7 GCPU Block Diagram Show it! 13 GCPU Show it! 14 University of Florida, File 04 7

8 The End! 15 University of Florida, File 04 8

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