Chapter 3 - Combinational Logic Design

A combinational circuit consists of logic gates whose
output is a function of only the present input.

Sequential logic is a type of logic circuit whose output
depends not only on the present value of its input signals but on the sequence of past inputs (state or memory).

3 Arithmetic Functions

简单的方法，2N个输入，N+1输出的encoder，比如两位加两位，看作四输入，输出3位
但这意味着输入变量会非常多

我们采用Iterative combinational circuitis，我们的核心思想是设计出一个处理单比特运算的“基本单元 (Cell)”，然后把许多个这样的单元像链条一样串联起来，组成“迭代阵列 (Iterative array)”

• The functional blocks for arithmetic are referred
  to as cells and the overall implementation is an
  array of cells.
• The iterative array is a method of calculating
  decomposition and takes advantage of the
  regularity to make a large and multiple-level
  arithmetic circuit design feasible.

3.1 Half-Adder

两输入的一位加法器

X	Y	S	C
0	0	0	0
0	1	1	0
1	0	1	0
1	1	0	1

In essence, a half-adder is a 2-to-2 encoder.
S(sum bit)是和，C(carry bit)是进位

当然S和C的表达方式有很多种，上面只是列举了最常见的一种

3.2 Full-Adder

A full adder is similar to a half adder, but includes a carry
in bit from lower stages. Like the half-adder, it computes a sum bit S, and a carry bit C.