A method for performing subtraction in binary arithmetic using the two’s complement representation of numbers offers a streamlined approach to digital circuit design. Rather than requiring separate circuitry for addition and subtraction, this technique allows subtraction to be accomplished through addition. For instance, to subtract 5 (0101 in binary) from 12 (1100 in binary) using this method, the two’s complement of 5 is first calculated (1011). Then, this two’s complement value is added to 12 (1100 + 1011 = 10111). Discarding the carry bit, the result is 0111, which represents 7 in decimal form, the correct answer.
The significance of employing this representation for subtraction lies in its simplification of arithmetic logic unit (ALU) design within computers and digital systems. By enabling subtraction to be performed using the same adder circuits used for addition, it reduces the complexity and cost associated with implementing separate subtractor circuits. Historically, this simplification proved crucial in early computer designs, contributing to more efficient and compact systems. The method continues to be vital in modern computing architectures.
