7 votes 7 votes If a 3 bit multiplicand is multiplied to a 2 bit multiplier, minimum number of two input AND, XOR, and OR gates, needed in the design are respectively?A) 16,14,1B) 7, 3, 1C) 10, 4, 1D) 8, 4, 1 Digital Logic digital-logic + – admin asked Sep 16, 2015 admin 5.6k views answer comment Share Follow See all 0 reply Please log in or register to add a comment.
Best answer 5 votes 5 votes let the three bit multiplicand be $111$ and two bit multiplier be $11$ $1 1 1$ $ * $ $1 1$ ${\color{Yellow} 1}$ ${\color{Green} 1}$ $1$ $1$ ${\color{Yellow} 1}$ ${\color{Green} 1}$ here we need 6 AND gates TO MULTIPLY ${\color{Red} 1}$ $0$ $1$ $0$ $1 $ TO ADD GREEN BITS WE NEED 1 HALF ADDER AND FOR YELLOW BIT WE NEED 1 FULL ADDER AND ONE MORE HALF ADDER FOR LAST BIT AS WE KNOW HALF ADDER NEEDS 1 XOR(FOR SUM) AND 1 AND GATE(FOR CARRY BIT) FULL ADDER NEED 2 XOR (FOR SUM)AND 2 AND GATE AND 1 OR GATE(FOR CARRY BIT) THEREFORE 2 HALF ADDER =2-XOR GATE +2 AND GATE 1 FULL ADDER =2-XOR GATE+2-AND GATE+1-OR GATE THEREFORE TOTAL 10 AND GATES 4 XOR GATES AND 1 OR GATE THEN IT WOULD BE 10 AND GATE 4 XOR GATE AND 1 OR GATE.(OPTION C) Umang Raman answered Sep 26, 2015 • edited May 18, 2020 by srestha Umang Raman comment Share Follow See all 13 Comments See all 13 13 Comments reply Pranay Datta 1 commented Nov 25, 2015 reply Follow Share i`m not getting . 6 and gate for the initials multiplication 1 half adder = 1 xor 1 and (for green) 1 full adder = 2 xor 2 and 1 or (for red ) 1 half adder =1 xor 1 and (if there is a carry from full adder ) so total 15 gates req . how 11 ? are we reusing any of these and gates ?? 0 votes 0 votes Umang Raman commented Nov 25, 2015 reply Follow Share 2 Half adder = 1 xor 1 and gate = 2 xor 2 and Full adder = 2 xor 3 and 1 or gate 6 and gate for the initials multiplication 11 And 4 XOR 1 OR 0 votes 0 votes Pranay Datta 1 commented Nov 25, 2015 reply Follow Share ok got that , thank you :) 0 votes 0 votes Pradip Nichite commented Jan 24, 2016 reply Follow Share in full adder , we have two AND gate not three 1 votes 1 votes Kapil commented Dec 18, 2016 reply Follow Share @Tendua How 10 AND gates ? It requires 6 AND gates, 2 HA and 2FA , right ? 0 votes 0 votes Tendua commented Dec 18, 2016 reply Follow Share 6 and gates are required apart from this a (2-1) 3 bit adder will be required but here the adder is not given so we have to make the addition using the half adder and full adders. To make a half adder 1 exor gate and 1 and gate . to make a full adder 2 exor 2 and and 1 or gate will be required. 0 votes 0 votes Akriti sood commented Dec 21, 2016 i edited by Akriti sood Dec 21, 2016 reply Follow Share http://faculty.kfupm.edu.sa/COE/abouh/Lesson3_3.pdf here it is given that number of addres required are (number of bits in multiplier -1) here,no. of bits in multilpier =2,so only 1 adder is required.. which is of 3 bits.dun we need 2 FA ansd 1 HA for 3 bit adder.??how is it 2 HA and 1 FA.?? 1 votes 1 votes Akriti sood commented Dec 21, 2016 i edited by Akriti sood Dec 21, 2016 reply Follow Share PLEASE SEE this figure..here B is multiplicand of 3 bits and A is multilpier of 2 bits.so ,can you tell through this figure how 2 HA and 1 FA is required cuz AFAIK,to make n bit addre,we can use n-1 FA na 1 HA.. please explain 0 votes 0 votes Tendua commented Dec 21, 2016 reply Follow Share Mam first see the best answer and read it again. And for making 3 bit adder in we may need a n-1 fa and one half adder at max. But here the hardware can be saved as the msb max only two bits can appear i.e( b2a1) and one carry if generated, So if max 2 is required a half adder will do the work so we have saved the hardware instead of applying a full adder. 1 votes 1 votes Akriti sood commented Dec 21, 2016 reply Follow Share yea..thanks..i got it. 0 votes 0 votes sushmita commented Jan 28, 2017 reply Follow Share CAN U FURTHER TELL THE TOTAL DELAY? 0 votes 0 votes sushmita commented Jan 28, 2017 reply Follow Share IT SHOULD BE 10 AND GATES RIGHT?? CAN SOMEONE PLZ TELL THE TOTAL DELAY TOO?? ASSUMING EVERY GATE HAS 1 UNIT OF DELAY.?? 0 votes 0 votes Kaluti commented Oct 8, 2017 reply Follow Share can someone elaborate more why do we need here 2 half adder and 1 full adder instead of 2 full adder and one half adder i am not getting it 1 votes 1 votes Please log in or register to add a comment.