Assembly Language Programming

Lesson 6: Binary Logic

By Robert M (adapted by Duane Alan Hahn)

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Table of Contents

Original Lesson

I know I promised to start discussing State Machines in Lesson 6, but now I see that I forgot to talk about binary logical functions. Since I just covered binary counting, and binary math; I think it would be best to push State Machines off to lesson 7 and cover binary logic now.






What is logic? I could spend days on that topic, so I need to focus on logic as it applied to programming computers. Recall our discussion of bits in Lesson 2. Each bit has one of two possible values 0 or 1. As the programmer you can apply any meaning you wish to each bit your program uses. A common use for bits is to indicate TRUE or FALSE. TRUE is usually represented by 1, and FALSE is represented by 0. Such an arrangement is called positive logic. You can also use negative logic, where TRUE is 0 and FALSE is 1. For this lesson I will confine the discussion to positive logic for all of the examples, since the instructions in the 650X microprocessors use positive logic.


For this class we are interested in logic functions that we can perform between pairs of bits representing TRUE and FALSE. Some interesting things can be done with bits using just a few simple logical rules.






Logic Functions

There are four basic logical functions: AND, OR, XOR, NOT. You can also combine NOT with the other 3 to form 3 more functions: NAND, NOR, and XNOR. I will discuss each logical function in detail.


Note: For all the experienced programmers reviewing this material, I decided to exclude the logical bit-shift operations from this lesson. I will cover bit-shifting and rotations when I cover those instructions.


The best way to think about binary logical functions is as a special math operator akin to adding and subtracting as we covered in the previous lesson. For all the logical operations, except NOT, there are 2 arguments and a single result. So like addition we can write logical operations as A (oper) B = C, where (oper) is the symbol of the logical function to be performed on A and B resulting in C.










  1. Given the following bytes (A) and bitmask (B) values calculate the result C, for C = A & B, C = A | B, and C = A ^ B.
    1. A = %11111111, B=%10101010
    2. A = %00000000, B=%01010101
    3. A = %11110000, B=%01110111


  2. Given the following bytes (A) and bitmask (B) values calculate the result C, for C = A NAND B, C = A NOR B, and C = A XNOR B.
    1. A = %10110110, B=%00000000
    2. A = %11111111, B=%11111111


  3. Fill in the blanks '_____' in this pseudocode example with what you believe is the correct logical function.

SUBROUTINE CheckPlayerStatus


        IF (PLAYER.has_green_key = TRUE) ___ (Player.is_touching_door) THEN

  Goto PlayerExitsLevel

        ELSE IF (Player.touching_monster = TRUE) ___ (Player.touching_arrow) THEN

  Goto PlayerKilled 

  ELSE IF (Player.touching_gold = TRUE) ___ (Monster.died) THEN

  Goto PlayerGetsPoints


END CheckPlayerStatus

  1. Bonus Puzzler!!!!
    You are running low on available memory for your game. You need to store 2 different counters of events occurring in your game. The first counter counts up from 0 to 7, when the counter reaches 7 the next time it is added to it resets to zero. The second counter, will count down from 13 to 0, once the counter is at zero it stays at zero even if it is decremented again. Devise a method for using binary addition and subtraction in combination with AND, OR, or NOR logic functions to allow you to store both counters in a single byte. You must be able to change either counter without affecting the other. Write the pseudo code to change each counter without affecting the other. Your solution must not share any bits between the two counters even though such a solution is technically possible, you do not have enough free clock cycles left in your program to use such a technique.







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Lesson Links

Lesson 1: Bits!

Lesson 2: Enumeration

Lesson 3: Codes

Lesson 4: Binary Counting

Lesson 5: Binary Math

Lesson 6: Binary Logic

Lesson 7: State Machines





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