Exercises

1. Using your favorite programming language, develop a simulation of a single-digit decimal adder that operates in the same manner as in Babbage's Analytical Engine. First, prompt the user for two digits in the range 0-9: the addend and the accumulator. Display the addend, the accumulator, and the carry, which is initially zero. Perform a series of cycles as follows:

   a. If the addend is zero, display the values of the addend, accumulator, and carry and terminate the program.

   b. Decrement the addend by one and increment the accumulator by one.

   c. If the accumulator incremented from nine to zero, increment the carry.

   d. Go back to step a.

   Test your code with these sums: 0+0, 0+1, 1+0, 1+2, 5+5, 9+1, and 9+9.

2. Create arrays of 40 decimal digits each for the addend, accumulator, and carry. Prompt the user for two decimal integers of up to 40 digits each. Perform the addition digit by digit using the cycles described in Exercise 1, and collect the carry output from each digit position in the carry array. After the cycles are complete, insert carries, and, where necessary, ripple them across digits to complete the addition operation. Display the results after each cycle and at the end. Test with the same sums as in Exercise 1 and test 99+1, 999999+1, 49+50, and 50+50.
3. Modify the program of Exercise 2 to implement subtraction of 40-digit decimal values. Perform borrowing as required. Test with 0-0, 1-0, 1000000-1, and 0-1. What is the result for 0-1?
4. 6502 assembly language references data in memory locations using an operand value containing the address (without the # character that indicates an immediate value). For example, the LDA $00 instruction loads the byte at memory address $00 into A. STA $01 stores the byte in A into address $01. Addresses can be any value in the range 0 to $FFFF, assuming memory exists at the address and the address is not already in use for some other purpose. Using your preferred 6502 emulator, write 6502 assembly code to store a 16-bit value into addresses $00-$01, store a second value into addresses $02-$03, then add the two values and store the result in $04-$05. Be sure to propagate any carry between the two bytes. Ignore any carry from the 16-bit result. Test with $0000+$0001, $00FF+$0001, and $1234+$5678.
5. Write 6502 assembly code to subtract two 16-bit values in a manner similar to Exercise 4. Test with $0001-$0000, $0001-$0001, $0100-$00FF, and $0000-$0001. What is the result for $0000-$0001?
6. Write 6502 assembly code to store two 32-bit integers to addresses $00-03 and $04-$07, then add them, storing the results in $08-$0B. Use a looping construct, including a label and a branch instruction, to iterate over the bytes of the two values to be added. Search the Internet for the details of the 6502 decrement and branch instructions and the use of labels in assembly language. Hint: The 6502 zero-page indexed addressing mode works well in this application.