Arithmetic

The Challenge: Multiplying 16-bit Numbers The Z80 performs 8-bit addition natively (ADD), but has no instruction for 16-bit multiplication (RR×RR). When you multiply two 16-bit numbers (like HL and DE), the result is a 32-bit number. We must build this algorithm using basic operations. The Algorithm: We use the same technique taught in grade school: break the numbers into parts, multiply each part, and sum the results. However, in assembly, it’s faster to use repeated shifting and conditional addition. ...

Arithmetic with Carry: ADC and SBC When adding numbers larger than 8 bits (like a 16-bit word or a 32-bit integer), you must add the Carry flag (C) from the previous operation into the current one. This is done with the ADC and SBC instructions. The Principle: Add (or Subtract) the current byte PLUS the Carry flag. Instruction Action Purpose ADC A, R A ← A + R + C Add with Carry: Used to link the result of the previous 8-bit addition. SBC A, R A ← A - R - C Subtract with Carry/Borrow: Used to link the result of the previous 8-bit subtraction. Example: 16-bit Addition (BC + DE) ...

Understanding Shifts and Rotations Shift and rotate instructions move the bits within a register. This is often done to perform arithmetic: shifting a number left by one position is equivalent to multiplying by 2, and shifting right is equivalent to integer dividing by 2. Key Difference: Shift: The bit that leaves one end is discarded, and a new bit (0 or the sign bit) enters the other end. Rotate: The bit that leaves one end wraps around to enter the other end, forming a circle. Arithmetic Shifts (SLA and SRA) Arithmetic shifts are best for multiplication and division because they handle the sign of the number correctly. ...