Analysis of Positive Logic and Negate Logic in 1bit adder and 4 bit adder 74LS283

1bit 전 가산기와 4bit 덧셈 연산기 74LS283에서 의정 논리와 부 논리에 대한 분석

1bit full adder have 3 input (including carry_in) and 2 outputs(Sum and Carry_out). Because of 1 bit full adder's propagation delay. We usually use 4-bit binary full adder with fast carry, 74LS283. The 74LS283 is positive logic circuit chip. But the logic function of binary adder is symmetrical, so it can be possible to use it not only positive logic but also the negative logic. This thesis use symmetrical property. such as $C_{i+1}(\bar{a_i}\bar{b_i}\bar{c_i})=C_{i+1}{\bar}(a_i,\;b_i,\;c_i)$ and $S_i(\bar{a_i}\bar{b_i}\bar{c_i})=\bar{S_i}(a_i,\;b_i,\;c_i)$. And prove this property with logic operation. Using these property, the 74LS283 adder is possile as the negation logic circuit. It's very useful to use the chip in negative logic. because many system chip is negative logic circuit. for example when we have negative logic chip with 74LS283. we don't need any not gate for 74LS283 input, and just use output of adder(74LS283) as the negation of original output.