1. Lecture 9 Topics: –Combinational circuits Basic concepts Examples of typical combinational circuits –Half-adder –Full-adder –Ripple-Carry adder –Decoder –Multiplexer –Bit shifter 1

2. Combinational Circuits Digital logic circuits can be categorized as: –Combinational circuits –Sequential circuits Combination logic is used to build circuits that contain basic Boolean operators, inputs and outputs. The key to recognize a combinational circuit –an output is always based entirely on the given inputs. Combinational circuit: –The output of a combinational circuit is a function of its inputs, –the output is uniquely determined by the values of the inputs at any given moments. 2

3. Half-Adder Half adder: –A typical combinational circuit –Adding two binary digits together. How to construct a half-adder? The truth table reveals that –Sum is actually an XOR. –Carry is equivalent to an AND gate. Combining an XOR gate and an AND gate results in the logic diagram for a half-adder. 3

4. Full-Adder 4

5. 5

6. Ripple-Carry Adder A full-adder is capable of adding only three bits. Full adders can connected in series to add binary numbers. This type of circuit is called a ripple-carry adder because of the sequential generation of carries that “ripple” through the adder stages. 6 Today’s systems employ more efficient adders.

7. 7 Decoders

8. Multiplexer 8

9. 9 A look Inside a Multiplexer with four inputs and two control lines A Multiplexer Symbol

10. 10 Bit Shifting moves the bits of a word or byte one position to the left or right. Bit Shifting A 4-bit shifter: When the control line, S, is low, left shift occurs; when S is high, right shift occurs.

11. 11 Bit Shifting moves the bits of a word or byte one position to the left or right. Bit Shifting - left A 4-bit shifter: When the control line, S, is low, left shift occurs; when S is high, right shift occurs. XX X

12. 12 Bit Shifting moves the bits of a word or byte one position to the left or right. Bit Shifting - right A 4-bit shifter: When the control line, S, is low, left shift occurs; when S is high, right shift occurs. X X X