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.
Fast 16x16-bit Multiplication (HL × DE)
This routine calculates Result (32-bit) = HL × DE. The 32-bit result will be stored across four registers (e.g., DEHL where DE is the high word and HL is the low word).
| Register Pair | Role |
|---|---|
| HL | Multiplicand (The first number). |
| DE | Multiplier (The second number). |
| BC | Accumulator for the 32-bit result (High Word). |
| Alternate Registers (HL’, DE’, BC’) | Used to hold the 32-bit accumulator (Low Word) temporarily. |
The Method (Simplified): We check each of the 16 bits in the Multiplier (DE). If a bit is set, we add the Multiplicand (HL) to the result, then we shift the result left by one position.
Key Instructions Used in 16x16 Multiply
| Instruction | Purpose in Multiplication |
|---|---|
ADD HL, DE |
The core addition of 16-bit values. |
RLC R / SLA R |
Shifting the multiplicand left to prepare it for the next bit position. |
JR C, label |
Checking the Carry Flag (C) after an addition to link the 16-bit result into the high 16-bit word. |
DJNZ |
Used for the main loop, repeating the process 16 times. |
Slower, but Easier to Write: For non-critical code, a much simpler approach is repeated addition: add the Multiplicand to itself ‘X’ times (where X is the Multiplier). This is compact but extremely slow.