IB CS Core — Topics 1–5 (SL & HL) · lesson 2 of 4 · 30 min
Binary, hexadecimal and number bases
topic: Topic 2
component:
Binary, hexadecimal, and number bases
Computers store all data in binary (base-2). Hexadecimal (base-16) is used as a compact human-readable representation of binary. The IB CS exam requires you to convert fluently between denary (base-10), binary, and hexadecimal.
Binary to denary conversion
Each binary digit has a place value that is a power of 2. Add the place values of all positions where the bit is 1. 128 + 32 + 16 + 4 + 1 = 181
Denary to binary conversion
Repeatedly divide by 2, recording remainders. Read remainders from bottom to top. Convert 75 to binary
75 ÷ 2 = 37 r 1 | 37 ÷ 2 = 18 r 1 | 18 ÷ 2 = 9 r 0
9 ÷ 2 = 4 r 1 | 4 ÷ 2 = 2 r 0 | 2 ÷ 2 = 1 r 0 | 1 ÷ 2 = 0 r 1
Result (bottom to top): 1001011
Verify: 64 + 8 + 2 + 1 = 75 ✓
Hexadecimal
Each hex digit represents exactly 4 binary bits (a nibble). To convert binary to hex, group bits into nibbles from the right and replace each with its hex equivalent. Convert 10111100 to hex
Group: 1011 | 1100
1011 = 11 = B 1100 = 12 = C
Result: BC
Verify: 11×16 + 12 = 176 + 12 = 188. Binary: 128+32+16+8+4 = 188 ✓
IB exam questions often ask you to show working. Always write out the nibble grouping and the conversion table — even if you can do it in your head.
Two’s complement
Two’s complement is the standard way to represent negative integers in binary. The most significant bit (MSB) is the sign bit: 0 = positive, 1 = negative. To negate a number: invert all bits, then add 1. Represent −45 in 8-bit two’s complement
45 in binary: 00101101
Invert all bits: 11010010
Add 1: 11010011
Verify: −128 + 64 + 16 + 2 + 1 = −128 + 83 = −45 ✓
Knowledge check
- Question of
- Hide hint
- Show hint
✓ Correct! ✕ Not quite
- Try again
- See results
- Next question
- Check answer
Previous lesson: CPU architecture: ALU, CU, registers, buses
Back to IB CS Core — Topics 1–5 (SL & HL)
Next lesson: Linear and binary search