Binary AdderSubtractorA Binary AdderSubtractor is a special type of circuit that is used to perform both operations, i.e., Addition and Subtraction. The operation which is going to be used depends on the values contained by the control signal. In Arithmetic Logical Unit, it is one of the most important components. To work with Binary AdderSubtractor, it is required that we have knowledge of the XOR gate, FullAdder, Binary Addition, and subtraction. For example, we will take two 4bit binary numbers 'X' and 'Y' for the operation with digits.
X_{0} X_{1} X_{2} X_{3} for X
Y_{0} Y_{1} Y_{2} Y_{3} for Y The Binary AdderSubtractor is a combination of 4 FullAdder, which is able to perform the addition and subtraction of 4bit binary numbers. The control line determines whether the operation being performed is either subtraction or addition. This determination is done by the binary values 0 and 1, which is hold by K. In the above diagram, the control lines of the first FullAdder is directly coming as its input(input carry C0). The X_{0} is the least significant bit of A, which is directly inputted in the FullAdder. The result produced by performing the XOR operation of Y_{0} and K is the third input of the Binary AdderSubtractor. The sum/difference(S_{0}) and carry(C_{0}) are the two outputs produced from the First Fulladder. When the value of K is set to true or 1, the Y_{0}⨁K produce the complement of Y_{0} as the output. So the operation would be X+Y_{0}', which is the 2's complement subtraction of X and Y. It means when the value of K is 1; the subtraction operation is performed by the binary AdderSubtractor. In the same way, when the value of K is set to 0, the Y_{0}⨁K produce Y_{0} as the output. So the operation would be X+Y_{0}, which is the binary addition of X and Y. It means when the value of K is 0; the addition operation is performed by the binary AdderSubtractor. The carry/borrow C_{0} is treated as the carry/borrow input for the second FullAdder. The sum/difference S_{0} defines the least significant bit of the sum/difference of numbers X and Y. Just like X_{0}, the X_{1}, X_{2}, and X_{3} are faded directly to the 2^{nd}, 3^{rd}, and 4^{th} FullAdder as an input. The outputs after performing the XOR operation of Y_{1}, Y_{2}, and Y_{3} inputs with K are the third inputs for 2^{nd}, 3^{rd}, and 4^{th} FullAdder. The carry C_{1}, C_{2} are passed as the input to the FullAdder. C_{out} is the output carry of the sum/difference. To form the final result, the S_{1}, S_{2}, S_{3} are recorded with s_{0}. We will use n number of FullAdder to design the nbit binary AdderSubtractor. Example: We assume that we have two 3 bit numbers, i.e., X=100 and Y=011, and feed them in FullAdder as an input. X_{0} = 0 X_{1} = 0 X_{2} = 1 Y_{0} = 1 Y_{1} = 1 & Y_{2} = 0 For K=0: Y_{0}⨁K=Y_{0} and C_{in}=K=0 So, from first FullAdder S_{0} = X_{0}+Y_{0}+C_{in} S_{0}= 0+1+0 S_{0}=1 C_{0}=0 Similarly, S_{1} = X_{1}+Y_{1}+C_{0} Similarly, S_{2} = X_{2}+Y_{2}+C_{1} Thus, X= 100 =4 For K=1 Y_{0}⨁K=Y_{0}' and C_{in}=k=1 So, S_{0} = X_{0}+Y_{0}'+C_{in} Similarly, S_{1} = X_{1}+Y_{1}'+C_{0} Similarly, S_{2} = X_{2}+Y_{2}'+C_{1} Thus, X = 010 = 4 Difference = 001 = 1
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