Understanding Binary and Hexadecimal

Easy Guide for Students

1. What is Binary?

Binary is a number system that only uses 0 and 1. Computers use binary to store and process information.

Students must be able to represent decimal values between 0 and 255 in binary.

Decimal 5 = Binary 00000101
Decimal 10 = Binary 00001010
Decimal 255 = Binary 11111111

Maximum 8-bit value:
Decimal: 255
Binary: 11111111

2. What is Hexadecimal?

Hexadecimal (Hex) is a number system that uses 16 symbols:

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F

After 9, we use letters: A = 10, B = 11, C = 12, D = 13, E = 14, F = 15

Students must be able to represent decimal values between 0 and 255 in hexadecimal.

Decimal 10 = Hex A
Decimal 15 = Hex F
Decimal 255 = Hex FF

Maximum value:
Decimal: 255
Hexadecimal: FF

3. Converting Between Number Systems

Binary ↔ Decimal

Binary 00001010 = Decimal 10
Binary 11111111 = Decimal 255

Decimal ↔ Hexadecimal

Decimal 15 = Hex F
Decimal 255 = Hex FF

Binary ↔ Hexadecimal

Each group of 4 binary digits equals one hex digit.

Binary 1111 = Hex F
Binary 11111111 = Hex FF

4. Important Maximum Values

Decimal: 255
Binary: 11111111
Hexadecimal: FF

These values are equivalent and represent the largest number possible using 8 bits.