Question

When subtracting two numbers, we also use the 2’s - complement system. The number to be subtracte d (the subtrahend) is changed to its 2’s - complement and then added to the minuend (the number the subtrahend is being subtracted from). Construct a circuit that performs this task. The input s of the circuit should be two four bit numbers of which the first bit is the sign bit and a control input which determines whether these number are added or subtracted from each other. Demonstrate that it works.

Answer 1

Solution: The circuit has to be design here needs to design here is a 2's complement calculator, whiclh takes a control signal to select whether addition or subtraction. If addition perform the normal addition and if subtraction, add 2's complement ofone with the other A 2*1 multiplexer can be used to select the operation that has to be performed Now use a full adder to perform the addition, use not gates to compute the 2's complement Let us mark the inputs as "A" and"B" both are four bits long and a control bit C to select the operation. C 1 for subtraction, C-0 for addition The circuit can be designed as given below.

2지 So Col Cio Csn . 2x1 TA 2x1 FA B2 FA 3

Operation: If C-0, then B input itself is passed into the full adder, thus the operation will be simple addition If C-0, then B input will be taken in complement form and then the C input is itself passed as carry Now the result will be A-B'+1, that is 2's complement addition will happen