Watch first — Craig 'n' Dave
Craig 'n' Dave · Edexcel 1CP2Binary and Number Systems
Interactive tool — this siteBinary converter, hex converter, addition, two's complement
Key facts
Converting between bases
- Binary → Denary: use place values 128, 64, 32, 16, 8, 4, 2, 1. Add up values where bit is 1.
- Denary → Binary: repeatedly divide by 2, read remainders bottom to top.
- Binary → Hex: split into nibbles (groups of 4 bits) from the right. Convert each nibble to one hex digit.
- Hex → Binary: convert each hex digit to 4 binary bits.
- Hex digits: 0-9 then A=10, B=11, C=12, D=13, E=14, F=15.
- Jun 2022 Q3(a)(i): 0011 1001. Jun 2023 Q5(d)(ii): 5B.
Arithmetic and shifts
- Binary addition: 0+0=0, 0+1=1, 1+0=1, 1+1=10 (carry 1), 1+1+1=11 (carry 1).
- Overflow: result too large for available bits. Result is incorrect.
- Two's complement: flip all bits then add 1. Used to represent negative numbers.
- Logical shift left: shift bits left, fill right with 0. Equivalent to ×2 per shift.
- Logical shift right: shift bits right, fill left with 0.
- Arithmetic shift right: shift right but copy the MSB (most significant bit) to preserve sign.
Why hexadecimal is used in computing
- Hex is a shorthand for binary — 2 hex digits = 1 byte (8 bits)
- Humans make fewer errors reading/writing hex than long binary strings
- Each hex digit maps to exactly 4 binary bits — easy conversion
- Used in: memory addresses, colour codes (#FF0000), MAC addresses, error codes
- Jun 2023 Specimen Q1(f)(ii): "hexadecimal is used as shorthand for binary — uses fewer digits — so humans make fewer mistakes"
- Do NOT say hex saves memory/storage — it doesn't; it's for human readability only.
Exam questions — 4 questions · 10 marks · from real 1CP2 past papers
1 markWhy hex is used1CP2 Specimen Q1(f)(ii) style
Why is hexadecimal used by programmers rather than binary?
A Hexadecimal uses less storage space than binary
B Hexadecimal is shorthand for binary — using fewer digits makes it easier for humans to read and reduces errors
C Hexadecimal is processed faster by the CPU
D Hexadecimal can represent more values than binary
2 marksBinary to hex conversion1CP2 Jun 2022 Q3(a)(i)-(ii) style
Convert the denary number 57 to binary. Then convert your binary answer to hexadecimal. Show your working. (2 marks)
Hint: Convert denary → binary using place values (128,64,32,16,8,4,2,1). Then split into two nibbles and convert each to one hex digit.
+20 XP
2 marksTwo's complement1CP2 Jun 2022 Q3(a)(iii) style
Describe how to find the two's complement of a binary number. (2 marks)
Hint: Two steps: (1) flip all bits → (2) add 1. Both steps needed for the mark.
+20 XP
1 markOverflow1CP2 Jun 2022 Q3(a)(iv) style
When adding two 8-bit binary numbers, what is an overflow error?
A When the result is negative
B When the result is too large to be stored in the available number of bits, causing an incorrect result
C When a bit is read incorrectly from memory
D When the CPU attempts to divide by zero
Module complete! 🎉
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