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The general process of multiplying two sets of two bits (a_{1} a_{0}) and (b_{1} b_{0}) is according to the following steps: In order to better understand the circuit of the set of two, two bits multiplier we draw the circuit with the half adder as a box, now we can see clearly way the calculations take place. 1) The result of the first multiplication is the value of c_{0} = a_{0}b_{0} (blue line). 2) Now perform the addition of c_{1} = a_{1} b_{0} ⨁ a_{0} b_{1}. This operation is performed by the half adder no. 1 circuit because it gets two values which are not including a carry from c_{0}. (see example 12). The result sum is the value of c_{1} (yellow line). 3) Now perform the addition of c_{2} = a_{1} b_{1} ⨁ carry. This operation is performed by the half adder no. 2 circuit notice that one input is the result of the carry from half adder number 1. The sum is the value of c_{2} (green line). 4) The result of the carry of the second adder is the value of c_{3} (red line). 


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