Summery

The subtraction of two binary numbers may be accomplished by taking the complement of the subtrahend and adding it to the minuhend. By this method, the subtraction operation becomes an addition operation requiring full adders for its machine implementation. It is possible to implement subtraction with logic circuits in a direct manner. By this method, each subtrahend bit of the number is subtracted from its corresponding significant minuhend bit to form a different bit. If the minuhend bit is smaller than the subtrahend bit, a 1 is borrowed from the next significant position. The fact that a 1 has been borrowed must be conveyed to the next higher pair of bits by means of a binary signal coming out (output) of a given stage and going into (input) the next higher stage. It is same for the half-adder and full -adder, half-subtractor and full-subtractor circuits.

A half-subtractor is a combinational circuit that subtracts two bits and produces their differences. It also has an output to specify if a 1 has been borrowed. Suppose the minuhend bit is x and the subtrahend bit is y. If we want to perform x-y, we have to check the relative magnitude between x and y. If x>/y, we have three possibilities:0-0=0, 1-0=1 and 1-1=0. The result is known as difference bit. If x<y we have 0-1, and its necessary to borrow 1 from the next higher stage. The borrowed 1 adds 2 to the minuhend bit. With the minuhend equal to 2, the difference becomes 2-1=1. The half-subtractor needs two outputs. One is needed to generate the difference and is denoted by the symbol D and the other is needed to show the borrowed bit and is denoted by the symbol B.

Truth Table

The truth table of half-subtractor circuit is given below

Input x | Input y | Output B | Output D |

0 | 0 | 0 | 0 |

0 | 1 | 1 | 1 |

1 | 1 | 0 | 1 |

1 | 1 | 0 | 0 |

Circuit Diagram

The Boolean functions for the two outputs of the half-subtractor circuit can be found directly from the truth table.

D=x'y+xy'

B=x'y

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