![]() With two’s complement, addition, subtraction, and multiplication all work as they do with positive binary numbers. The standard approach is two’s complement, as with almost all CPUs and software. If your design requires negative values, you need to handle signed numbers. You can nest concat operators, as in the final example above.Ĭoncat allows us to set an appropriate value regardless of the vector width. Localparam CORDW = 12 // coordinate width in bits ![]() Let’s take a look at 42 in binary: 101010 2 Simple, right?įor positive integers, things are pretty straightforward. BinaryĬomputers famously “think” in binary, and the same is true for most electronics. How many bits do I need? Do I need signed numbers? Will BCD make my design simpler? Is fixed-point accurate enough? What happens when I mix different widths in one expression?įor something a bit less ordinary, try Cistercian numerals (Wikipedia). We’re so familiar with different representations of numbers we hardly give them a second thought.ĭifferent representations express (almost) the same thing but work better (or worse) in different circumstances: hexadecimal is suitable for a memory address, while scientific notation compactly expresses vast and tiny numbers alike.Īs a hardware designer, you need to consider how you represent numbers.
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