试用一片3-8译码器74LS138和其它必要的门电路设计一个一位全加器, 被加数为Ai, 加数为Bi, 低位来的进位为Ci-1, 本位和为Si, 本位对高位的进位为Ci
(1)根据题目的描述, 列出真值表.
| 一位全加器真值表 | ||||
| Ai | Bi | Ci-1 | Si | Ci |
| 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 1 | 0 |
| 0 | 1 | 0 | 1 | 0 |
| 0 | 1 | 1 | 0 | 1 |
| 1 | 0 | 0 | 1 | 0 |
| 1 | 0 | 1 | 0 | 1 |
| 1 | 1 | 0 | 0 | 1 |
| 1 | 1 | 1 | 1 | 1 |
(2)写出Si和Ci的表达式.
Si(Ai,Bi,Ci-1)=∑m(1,2,4,7)=m1+m2+m4+m7.
Ci(Ai,Bi,Ci-1)=∑m(3,5,6,7)=m3+m5+m6+m7.
(3)画出电路原理图.
Si(Ai,Bi,Ci-1)=∑m(1,2,4,7)=m1+m2+m4+m7=((m1+m2+m4+m7)')'=(m1'·m2'·m4'·m7')'=(Y1'·Y2'·Y4'·Y7')'.
Ci(Ai,Bi,Ci-1)=∑m(3,5,6,7)=m3+m5+m6+m7=((m3+m5+m6+m7)')'=(m3'·m5'·m6'·m7')'=(Y3'·Y5'·Y6'·Y7')'.