Binary and hexadecimal
Translate between compact hexadecimal notation and bit patterns.
What you will learn
- Convert binary nibbles to hexadecimal.
- Check a result using denary place values.
One hex digit represents four bits
Hexadecimal is base 16 and uses digits 0–9 and letters A–F for values 10–15. Four binary bits have 16 possible patterns, so each group maps directly to one hexadecimal digit.
Group bits from the right. Add leading zeros to complete the leftmost group when necessary. Do not add zeros on the right because that changes the value.
Check with place values
Two hexadecimal digits XY represent 16×X+Y. You can compare that denary value with the binary place-value total as an independent check.
If asked for two hexadecimal digits, write the two digits themselves. A prefix such as 0x identifies notation in some programming languages but is not one of the two digits.
Worked example
Convert binary 10111100 to hexadecimal.
Show the worked solution
- Split into 1011 and 1100.
- 1011=11=B and 1100=12=C.
- Check: 11×16+12=188, equal to 128+32+16+8+4.
Answer BC
Common mistakes
- Group from the right rather than making arbitrary groups.
- The letters represent values above nine, not additional bits.
What can you explain now?
Write hexadecimal 3F in eight-bit binary.
Compare with the explanation
00111111
3 maps to 0011 and F to 1111.
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