Digital Systems

Insights

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  Binary, hex and decimal

  Why one value has three names, and how to switch between them.

  3 min read

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  1's and 2's complement

  How a fixed number of bits stores negative numbers.

  3 min read

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  Gray code, BCD and parity

  Three ways to code a number so hardware can use it safely.

  3 min read

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  Binary addition and subtraction

  Carry, overflow, and why subtracting is adding a negative.

  3 min read

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  Multiply, divide and modulus

  Shifts and masks: the cheap way to scale by powers of two.

  3 min read

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  Logic gates

  AND, OR, NOT, XOR and friends: the circuits behind every bit operator.

  3 min read

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  Boolean algebra

  The few laws that simplify logic, and De Morgan's rule for conditions.

  3 min read

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  Multiplexers and decoders

  Pick one of many, or switch on one of many, with select lines.

  3 min read

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  Half and full adders

  Two gates add one bit; chain them and you have an ALU's adder.

  3 min read

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  Latches and flip-flops

  How gates remember one bit, and why the clock edge matters.

  4 min read

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  Registers and counters

  Flip-flops in a row hold a byte, shift it, or count with it.

  3 min read

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  ADC and DAC

  Where digital meets the analog world: samples in, voltages out.

  4 min read