1. Write a program in LC-3 assembly language that computes Fn, the nth Fibonacci number.

2. Find the largest Fn such that no overflow occurs, i.e. find n = N such that FN is the largest Fibonacci number to be correctly represented with 16 bits in twos complement format.

FIBONACCI NUMBERS 4.1 Problem Statement 1. Write a program in LC-3 assembly language that computes F, the n-th Fibonacci number 2. Find the largest Fn such that no overflow occurs, i.e. find N such that Fv is the largest Fibonacci number to be correctly represented with 16 bits in two's complement format. 4.1.1 Inputs The integer n is in memory location x3100: x3100in 4.1.2 Outputs x3101F x3102 |N x3103 Fv 4.2 Example x31006 x3101 8 x3102 |N x3103 Fv Starting with 6 in location x3100 means that we intend to compute Fo and place that result in location x3101. Indeed, F6-8. (See below.) The actual values of N and Fv should be found by your program, and be placed in their corresponding locations. 4.3 Fibonacci Numbers The Fibonacci F numbers are the members of the Fibonacci sequence: 1,1,2,3.5,8,.... The first two are explicitly defined: Fi F21. The rest are defined according to this recursive formula: F-F-1 +F-2. In words, each Fibonacci number is the sum of the two previous ones in the Fibonacci sequence. From the sequence above we see that F6 8 Revision: 1.8, August 14, 2005 4-1 FIBONACCI NUMBERS 4.1 Problem Statement 1. Write a program in LC-3 assembly language that computes F, the n-th Fibonacci number 2. Find the largest Fn such that no overflow occurs, i.e. find N such that Fv is the largest Fibonacci number to be correctly represented with 16 bits in two's complement format. 4.1.1 Inputs The integer n is in memory location x3100: x3100in 4.1.2 Outputs x3101F x3102 |N x3103 Fv 4.2 Example x31006 x3101 8 x3102 |N x3103 Fv Starting with 6 in location x3100 means that we intend to compute Fo and place that result in location x3101. Indeed, F6-8. (See below.) The actual values of N and Fv should be found by your program, and be placed in their corresponding locations. 4.3 Fibonacci Numbers The Fibonacci F numbers are the members of the Fibonacci sequence: 1,1,2,3.5,8,.... The first two are explicitly defined: Fi F21. The rest are defined according to this recursive formula: F-F-1 +F-2. In words, each Fibonacci number is the sum of the two previous ones in the Fibonacci sequence. From the sequence above we see that F6 8 Revision: 1.8, August 14, 2005 4-1