Cambridge Syllabus Notes

Data Representation: Two’s Complement for 8‑bit Integers

Objective 🎯

Use the two’s complement number system to represent positive and negative 8‑bit binary integers.

What is Two’s Complement? 🤔

In binary, the leftmost bit (most significant bit) is the sign bit.
• 0 → positive number
• 1 → negative number Two’s complement lets us store negative numbers in the same 8‑bit format as positives.

How to Convert a Decimal to 8‑bit Two’s Complement

Write the decimal number in binary (ignore the sign for now).
If the number is negative, invert all bits (change 0→1, 1→0).
Add 1 to the inverted binary number.
Keep only the lowest 8 bits (drop any overflow).

Example: Convert –5 to 8‑bit two’s complement.
1️⃣ 5 in binary: 00000101
2️⃣ Invert: 11111010
3️⃣ Add 1: 11111011
Result: 11111011 (which equals –5 in two’s complement)

Examples Table 📊

Decimal	Binary (8‑bit)	Two’s Complement
+12	00001100	00001100
–12	11110011	11110011
+255	11111111	11111111
–1	11111110	11111111

Exam Tips for IGCSE 0478 📚

Remember: Leftmost bit = sign. 0 = positive, 1 = negative.
When converting negatives, invert then add 1. A quick mental trick: “flip and bump.”
Check overflow: only keep the lowest 8 bits.
Practice converting both ways: decimal → binary → two’s complement, and two’s complement → decimal.
Use the 2⁸ = 256 rule: the range of 8‑bit two’s complement is –128 to +127.

Quick Practice Problems ??

Convert +42 to 8‑bit two’s complement.
Convert –100 to 8‑bit two’s complement.
What is the decimal value of binary 11001010 in two’s complement?
Show the steps to convert –15 to binary.

Tip: Write down each step; examiners love clear, logical reasoning. Good luck! 🚀

Use the two’s complement number system to represent positive and negative 8-bit binary integers