1.4 Data types, data structures and algorithms

Truth tables

Show all the possible outcomes for a particular operation.

K-maps

Every group in a K-map must be a rectangle and a power of 2 (1,2,4,8 etc). An element can be in more than one group; this can also provide better precision.

Logic gates:

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Negates input.

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If both inputs are true, the statement is true.

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If one input is true, the statement is true.

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Same as OR, but if both inputs are true, the statement is false.

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Negates OR.

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Negates AND.

Simplifying circuits:

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Unsigned integers:

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Have column headings as powers of 10.

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Have column headings as powers of 2.

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Have column headings as powers of 16 (0-9, A-F).

Adders:

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2 bits added.

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3 bits added, taking in a carry.

Sign and magnitude

Unsigned binary cannot represent negative numbers. In S+M, the MSB represents a negative sign.

2's Complement

Replaces the MSB with a negative value. In a byte, this would be -128 instead of 128.

Adding negative numbers

Using two's complement, add the numbers together with a negative version.

Floating point

Express a number in floating point format.

Precision

Refers to how many significant figures a number has.

Accuracy

Refers to how correct a number is.

Adding floating point numbers

Make the exponents the same, then add the mantissas. Ignore overflow if carry in and out are the same with 2's complement.