Computer Org Lecture 7 Name 1 Sum the following binary base 2 numbers 100112 101102 1011012 1101112 2 Complete the Full Adder truth table for the sum si and carry out ci 1 functions carry in sum carry out ci si xi yi ci 1 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1 3 Use k maps to minimize the sum si and carry out ci 1 functions of the Full Adder 4 For the one bit Full Adder how many gate delays are needed before the carry out ci 1 wire is correct 5 A 32 bit ripple adder is made up of a collection of single bit Full Adders connected together as shown below x 31 x 1 y 31 C 31 C 32 Sum y 1 y 0 0 C0 C1 C2 31 x 0 Sum 1 Sum 0 How many gate delays are needed before c32 is correct Lecture 7 Page 1 Computer Org Lecture 7 Name 6 To speed up the calculation of the carry out Ci 1 signals consider constructing a 32 bit adder using two bit adders as shown in x 31 y 31 x 30 y 30 C 32 Sum C 30 31 Sum 30 x i yi C i 1 Sum x i 1y i 1 C i 1 i Sum i 1 x 1 y1 C2 Sum x 0 y0 C0 1 Sum 0 0 If ci 1 is calculated directly from the inputs as c i 1 xi yi xi xi 1 yi 1 xi xi 1 ci 1 xi yi 1 ci 1 yi xi 1 yi 1 yi xi 1 ci 1 yi yi 1 ci 1 then how many gate delays would be needed to calculate the ci 1 signal in a two bit adder 7 What would be the total number of gate delays in a 32 bit adder before the c 32 signal is generated correctly if two bit adders were used 8 What would be the total number of gate delays in a 32 bit adder before the c 32 signal is generated correctly if three bit adders were used 10 three bit adders and a 2 bit adder 9 What would be the total number of gate delays in a 32 bit adder before the c 32 signal is generated correctly if four bit adders were used Lecture 7 Page 2
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