Digital Arithmetic

58 C H A Pl" E R 2 Two-Operand Addition

EXAMPLE 2.1

These expressions 2 are the basis for linear and treelike structures to obtain all the

carries. These structures are the main topic of this chapter.

Once all the carries are obtained, the sum bits are computed in parallel as:

S i "~ Xi f~

Yi

f~ ci -- Pi ~ ci

2.21

We now illustrate the use of these expressions to obtain bit 13 of the sum 3 of

the following 16-bit operands

(Cin

-- 0):

x -- 01101001011100[0011

y- 1011lll01[0001[lll0

m

First we need to obtain the carry c13. To do this we divide the operands in

groups of four bits, and for each group we obtain (in parallel) the ...