1. ReturnNext  Half adder, adds two 1-bit operands x and y, producing a 2-bit sum. The low- order bit of the sum may be named HS (half sum), and the high-order bit may be named CO (carry out)  Half Adders and Full Adders 5.10 Adders, Subtractor and ALUs HS=X ⊕ Y= X·Y+X ·Y CO=X·Y

2.  Full adder, Besides the addend-bit inputs x and y, a full adder has a carry-bit input, CIN. And two output bits, S and COUT. 5.10 Adders, Subtractor and ALUs COUT=X·Y+X·CIN+Y·CIN S=X ⊕ Y ⊕ CIN =X·Y·CIN+X·Y·CIN+X·Y·CIN+X·Y·CIN (p431 Figure 5-86) NextBackReturn

3.  Ripple Adders  Two binary words, each with n bits,can be added using a ripple adder----a cascade of n full-adder stages, each of which handles one bit. 5.10 Adders, Subtractor and ALUs  A ripple adder is slow, the total worst- case delay is t ADD =t XYCout +(n-2) · t CinCout +t CinS (p432 Figure 5-87) BackReturn