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Digital Logic Circuits By : Tamsil Shamsi

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Page 1: Digital logic circuit

Digital Logic Circuits

By : Tamsil Shamsi

Page 2: Digital logic circuit

Half Adder

Logic Diagram

Truth Table

A half adder adds two one-bit binary numbers A and B. It has two outputs, S and C.

The simplest half-adder design, pictured on the right, incorporates an XOR gate for S and an AND gate for C. Half adders cannot be used compositely, given their incapacity for a carry-in bit.

http://en.wikipedia.org/wiki/XOR_gate
http://en.wikipedia.org/wiki/AND_gate
Page 3: Digital logic circuit

Full AdderA full adder adds binary numbers and accounts for values carried in as well as out. A one-bit full adder adds three one-bit numbers, often written as A, B, and Cin; A and B are the operands, and Cin is a bit carried in.

A full adder can be constructed from two half adders by connecting A and B to the input of one half adder, connecting the sum from that to an input to the second adder, connecting Cin to the other input and OR the two carry outputs

Logic Diagram

Truth Table

Page 4: Digital logic circuit

SR Flip-Flop

Graphic Symbol

Truth Table

A SR flip-flop has three inputs, S (for set), R (for reset) and C (for clock). It has an output Q.

The undefined condition makes the SR flip-flop difficult to manage and therefore it is seldom used in practice.

Page 5: Digital logic circuit

D Flip-Flop

Graphic Symbol

Truth Table

The D flip-flop is a slight modification of the SR flip-flop by inserting an inverter between S and R and assigning the symbol D to the single input.

If D=1, the output goes to the state 1, and if D=0, the output of the flip flop goes to the 0 state.

Page 6: Digital logic circuit

JK Flip-Flop

Graphic Symbol

Truth Table

Inputs J and K behave like inputs S and R. When inputs J and K are both equal to 1, a clock transition switches the output of the flip-flop to their complement state.

Page 7: Digital logic circuit

T Flip-Flop

Truth Table

Graphic Symbol

The T flip-flop is obtained from a JK flip-flop when inputs J and K are connected to provide a single input designated by T.

The flip-flop thus has only two conditions.

Page 8: Digital logic circuit

Excitation Tables During the design of circuits, we need a table that lists the required input combinations for a given change of state. Such table is called a flip flop excitation table.

Page 9: Digital logic circuit

Sequential Circuits• A sequential circuit

is an interconnection of flip-flops and gates.

Example of a Sequential Circuit

Ax

Bx

Ax+Bx

A’x

x’

A+B (A+B).x

A=Ax+Bx, B=A’x

y=(A+B).x

State Table


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