1.7a - Binary Math (Prof. Messer)

Vocabulary and core concepts for binary-to-decimal and decimal-to-binary conversion as applied to IP subnetting.

Binary

A type of numbering that uses two different numbers, either a 0 or a 1.

Bit

Each individual 0 or 1 used in binary numbering.

Byte

A combination of eight bits.

Octet

A term used to refer to a byte to ensure it is understood as containing 8 bits.

Binary-to-Decimal Conversion Chart

A chart created by starting with 1 on the right and doubling the number as you move to the left: 1, 2, 4, 8, 16, 32, 64, 128.

Binary 00000010

The binary value equivalent to 2 in decimal.

Binary 10000010

The binary value equivalent to 130 in decimal ($128 + 2$).

Binary 11111111

The binary value equivalent to 255 in decimal ($128 + 64 + 32 + 16 + 8 + 4 + 2 + 1$).

Decimal 154 in Binary

The decimal value 154 is equivalent to 10011010 in binary.

2 bits

A binary length that provides four possible outcomes: 00, 01, 10, and 11 (decimal 0, 1, 2, and 3).

3 bits

A binary length that provides eight possible outcomes.

4 bits

A binary length that provides 16 different options.

5 bits

A binary length that provides 32 possible outcomes.

6 bits

A binary length that provides 64 possible outcomes.

7 bits

A binary length that provides 128 possible options.

Powers of 2

The mathematical basis for binary placeholders where $2^0 = 1$, $2^1 = 2$, $2^2 = 4$, $2^3 = 8$, and so on.