Knowledge Organiser: Binary and Hexadecimal
Key Terms
- Binary: Base 2 number system using only 0s and 1s
- Denary/Decimal: Base 10 number system (everyday counting)
- Hexadecimal: Base 16 number system using 0-9 and A-F
- Bit: A single binary digit (0 or 1)
- Nibble: 4 bits (represents exactly one hex digit)
- Byte: 8 bits (two hex digits)
- MSB: Most Significant Bit (leftmost, highest place value)
Must-Know Facts
- 8-bit binary place values: 128, 64, 32, 16, 8, 4, 2, 1
- Hex letters: A=10, B=11, C=12, D=13, E=14, F=15
- 1 hex digit = exactly 4 binary bits
- 8-bit range: 0 to 255 (00 to FF in hex)
- Hex is used for: memory addresses, colour codes (#FF5733), MAC addresses
- To convert binary to hex: group into 4-bit nibbles from the right
- To convert hex to binary: expand each digit to 4 bits (pad with leading 0s)
Key Concepts
- Binary to denary: Add place values where bit = 1 (e.g. 1011 = 8+2+1 = 11)
- Denary to binary: Find largest fitting place value, subtract and repeat
- Binary to hex: Group in 4s, convert each group (1101 0110 = D6)
- Hex to binary: Each hex digit becomes 4 bits (3A = 0011 1010)
- Hex to denary: Multiply each digit by its 16n place value (3F = 48+15 = 63)
- Why hex? Shorthand for binary — more compact and readable for humans
Common Mistakes
- Forgetting to pad hex digits to 4 bits: Each hex digit must expand to exactly 4 binary bits — 3 must become 0011, not just 11
- Wrong place values in binary: The 8-bit place values are 128, 64, 32, 16, 8, 4, 2, 1 — students often mix up the order or miss the 128 column
- Confusing hex letters with denary values: A=10, B=11, C=12, D=13, E=14, F=15 — forgetting that F represents 15, not 6
- Not grouping from the right when converting binary to hex: Always split binary into groups of 4 starting from the RIGHT (least significant end), padding with zeros on the left if needed