Unit IV Adders Subtractors Flip Flops Counters Multiplexes and De multiplexes. Integrated circuits-Op. amp – Characteristics Inverting amplifier - Non-inverting amplifier Differentiator & integrator- I/V converter & V/I converter Instrumentation amplifier - filters using op-Amp

2019/10/31 PJF- 2 Combinational Logic Combinational Circuits A combinational circuit consists of logic gates whose outputs, at any time, are determined by combining the values of the inputs. For n input variables, there are 2 n possible binary input combinations. For each binary combination of the input variables, there is one possible output.

2019/10/31 PJF- 3 Combinational Logic Combinational Circuits (cont.) Hence, a combinational circuit can be described by: 1.A truth table that lists the output values for each combination of the input variables, or 2.m Boolean functions, one for each output variable. Combinational Circuit n-inputsm-outputs

2019/10/31 PJF- 4 Combinational Logic Combinational vs. Sequential Circuits Combinational circuits are memory-less. Thus, the output value depends ONLY on the current input values. Sequential circuits consist of combinational logic as well as memory elements (used to store certain circuit states). Outputs depend on BOTH current input values and previous input values (kept in the storage elements).

Combinational vs. Sequential Circuits Combinational Circuit n-inputsm-outputs (Depend only on inputs) Combinational Circuit n-inputsm-outputs Storage Elements Next state Present state Sequential Circuit Combinational Circuit

Conceptually similar to decimal addition Binary adder that produces the arithmetic sum of binary numbers can be constructed with 1.Half adders and 2. Full adders Binary adder Half Adder (single bit adder) A combinational logic circuit that performs the addition of two data bits, A and B, is called a half-adder. Addition will result in two output bits; one of which is the sum bit, S, and the other is the carry bit, C. Only adds Least Significant Digit (LSD) column (1s column) in binary addition

Half Adder (contd……) A B  (sum) C 0 (carry out) Half Adder Input Output Logic Symbol: Logic Diagram:

 A combinational logic circuit that adds two data bits, A and B, and a carry-in bit, Cin, is called a full-adder  Used for adding binary place values other than the 1s place  The difference between a full adder and a half adder we looked at is that a full adder accepts inputs A and B plus a carry-in (Cin) giving outputs Q and Cout. Full Adder Logic Symbol: A B  (sum) C 0 (carry out) Full Adder Input Output C in

C0Cin AB Cin AB Cin Q=Cin’(A’B+AB’)+Cin(A’B’+AB) Co=AB+Bcin+ACin

Logic Diagram Q=Cin’(A’B+AB’)+Cin(A’B’+AB) Co=AB+BCin+ACin A’ B’ Cin A’ B Cin’ A B’ Cin’ A B Cin ABAB B Cin A Cin

Subtraction can be performed using binary numbers. Subtracting a single-bit binary value B from another A (i.e. A -B ) produces a difference bit Q and a borrow bit Bin Binary Subtractors Truth Table For Half Subtractor Logic diagram for half subtractor Q=AB’+A’BBin= A’B

Binary full subtractor Truth table and logic diagram for full subtractor

2019/10/31 PJF- 14 Combinational Logic Integrated Circuits Integrated circuit (a chip) is a semiconductor crystal (most often silicon) containing the electronic components for the digital gates and storage elements which are interconnected on the chip. Terminology - Levels of chip integration – SSI (small-scale integrated) - fewer than 10 gates – MSI (medium-scale integrated) - 10 to 100 gates – LSI (large-scale integrated) to thousands of gates – VLSI (very large-scale integrated) - thousands to 100s of millions of gates