Karnaugh map is a systematic method for simplifying and manipulating switching expressions.
It is used to represent the information contained in a truth table or the information available in the form of POS or SOP. The characteristics of a K-map are:
In an n-variable K-map, there are 2 n cells and each cell matched to one combination of n variables.
In an n-variable K-map, a collection of 2 m cells and each adjacent to m cells is known as a group.This group can be expressed by a product containing n-m variables where n is the number of variables in the K-map.
Logic circuit consists of three elements, which are:
Input variables : The input variables are the inputs to the logic circuits, which are represented by 1 and 0. The input 1 implies the high voltage (High) or +5V and input 0 implies the low voltage (Low) or 0V.
Output variables : The output variables are the resultant outputs of the two input variables. The resultant output depends upon the type of logic gate that is being used.
Logic gate : A logic gate is an electronic circuit that has two inputs and one output. At any instant, every input is in one of the two binary conditions such as 0 and 1.
DTL family removes the problem of output voltage by increasing the load on the circuit.
If the inputs to the diodes are HIGH, they are reverse-biased. If both the diodes and the transistors are switched ON, then the output is LOW.
If any of the inputs to the diodes is LOW, the current flows through the other diode and the voltage to that diode drops down. Then, the base voltage becomes LOW and the transistor remains at logic 0 and the output is HIGH.
Flip-flops are primarily used in counter circuits, frequency dividers, shift and storage registers.
It can also help in accomplishing serial decoding, comparison and timing functions.
Other functions of flip-flops include:
Frequency Division : Flip-flops are used to divide the frequency of a periodic waveform.
Shift Registers : Flip-flops are used in shift Registers for transferring the contents of one register to the other. If the flip-flop lies within the same register, then shifting takes place in one bit at a time.
Up-down Counter is a combination of up and down counter.
It can count upwards as well as downwards.
It is also called multimode counter.
It uses logic gates to allow either the inverted or non-inverted output of one flip-flop to the clock input of the next flip-flop, depending upon the status of control inputs.
If the control inputs are both 1 or 0, then the counter does not count upwards or downwards, because the clock inputs of all the flip-flops except, the LSB will be held constant at either 0 or 1. This condition is avoided.