Step 1: BINARY TO 9’s COMPLEMENT
BINARY TO 9’s COMPLEMENT
To design and verify four bits binary to 9’s complement converter circuit.
Hardware Requirement: -
a. Equipment – Digital IC Trainer Kit
b. Discrete Components – 74LS86 EX-OR gate
74LS04 NOT gate
74LS08 AND gate
The conversion from one code to another is common in digital systems. Sometimes the output of a system is used as the input to the other systems.
The availability of large variety of codes for the same discrete elements of information results in the use of different codes by different systems. A conversion circuit must be inserted between the two systems if each uses different codes for same information. Thus, code converter is a circuit that makes the two systems compatible even though each uses different binary codes. The bit combination assigned to binary code to 9’s complement. Since each code uses four bits to represent a decimal digit. There are four inputs and outputs. The inputs variable is designated as A, B, C, D and the output variables are W, X, Y, Z from the truth table, combinational circuit is designed. The Boolean functions are obtained from K-Map for each output variable.
Binary to 9’s Complement conversion: -
To obtain the 9’s complement of any number we have to subtract the number with (-1) where n=number of digits in a number.
Examples: - Consider the decimal number 8.
Binary code: - 1000
9’s complement: - 0001
Boolean equation from truth table: -
W=A’B’C’D’+A’B’C’D=A’B’C’(D’+D) = A’B’C’
1. Using the derived expressions, implement binary to 9’s complement convertor using logic gates and verify its functional table.
2. The inputs A, B, C, D are given at respective pins and outputs W, X, Y, Z are taken for all the 10 combinations of inputs.
GIVEN ABOVE IS THE CIRCUIT DIAGRAM OF THE IC'S HERE WE HAVE USED XOR GATE AND NAND GATE CONNECT THE CIRCUIT AS SHOWN ABOVE.
THE TRUTH TABLE OF THE ABOVE CIRCUIT DIAGRAM IS SHOWN, AS WE KNOW THAT 9S COMPLEMENT OF A NUMBER CAN BE FIND OUT BY SUBTRACTING IT FROM 9999.SO IF WE WISH TO FIND OUT THE 9S COMPLEMENT OF THE 8 THEN WE GET 1.
HERE IS THE MAIN COMPONENT WE NEED FOR MAKING OUR PROJECT THIS IS AN IC DICK.
AN IC DICK CONSISTS OF A BREADBOARD ,POWER SUPPLY SOURCE AND VARIOUS FUNCTION SYSTEMS LIKE CLOCK PULSE, TRIGGERING PULSE AND OTHER KEYS THAT I WILL DISCUSS OTHER TIME,OUR MAIN FOCUS IS TO CONNECT THE IC TO BREADBOARD AND THEN TO THE INPUT AND OUTPUT BUTTON OF THE DICK AS SHOWN IN FIG.
HERE IS THE PIN CIRCUIT DIAGRAM OF THE IC OF ALL GATES BUT SINCE WE ARE USING NOT ,AND AND OR GATE WE WILL BE CONCENTRATING ON IT CONNECT THE IC'S AS GIVEN IN THE PIN DIAGRAM NOTE THAT THE 1ST PIN IS CONNECTED TO 5V OF IC DICK AND 7TH PIN IS CONNECTED TO GROUND OF DICK.
after all the connection is done in ic kit then we will verify our result now the 9s complement of the number can be find out by subtracting from 9 so if we wish to find out the 9s complement of 1 we will switch on the the 1st button of the kit and as the 1st button will switch on the ic the 8 th led of the kit will glow up this verifies our experiment.