Binary

Binary digit '1' electrical state

ON state / High voltage signal.

Binary digit '0' electrical state

OFF state / Low or zero voltage signal.

Definition of a bit

The smallest unit of digital data, representing a single binary choice of 0 or 1.

Definition of a byte

A standard sequence of exactly 8 bits grouped together.

Formula for total unique combinations using n bits

2^n, where n represents the total number of bits or switches.

Total unique combinations possible with 2 binary switches

4 unique combinations (00, 01, 10, 11).

Total unique combinations possible with 3 binary switches

8 unique combinations (2^3 = 8), ranging from decimal values 0 to 7.

Total unique combinations possible with 4 binary switches

16 unique combinations (2^4 = 16), ranging from decimal values 0 to 15.

Binary representation of the decimal number 2

10 (Twos column is active, Ones column is inactive)

Binary representation of the decimal number 4

100 (Fours column is active, Twos and Ones columns are inactive)

Binary representation of the decimal number 5

101 (4 + 1 = 5)

Binary representation of the decimal number 8

1000 (Eights column is active, all others are inactive)

Value of the 1st binary column (far right)

1 (The Ones column)

Value of the 2nd binary column from the right

2 (The Twos column)

Value of the 5th binary column from the right

16 (The Sixteens column)

Value of the 7th binary column from the right

64 (The Sixty-Fours column)

Value of the 8th (leftmost) column in a single byte

128 (The One-Twenty-Eights column)

Value of the 9th binary column from the right

256 (The Two-Fifty-Sixes column)

Maximum decimal value of a 2-digit binary number (11)

3 (2 + 1 = 3)

Maximum decimal value of a 3-digit binary number (111)

7 (4 + 2 + 1 = 7)

Maximum decimal value of a 4-digit binary number (1111)

15 (8 + 4 + 2 + 1 = 15)

Output condition for an AND Gate

Outputs a 1 only when BOTH inputs are 1. Outputs a 0 under all other conditions.

Output condition for an OR Gate

Outputs a 1 if AT LEAST ONE input is 1. Outputs a 0 only when both inputs are 0.

ASCII code purpose

A standard code that maps specific binary numbers (0 to 255) to text characters and keyboard symbols.

Growth pattern of binary column values moving right to left

Each successive column value doubles (1, 2, 4, 8, 16…).