← IGCSE Computer Science Paper 1

The sign bit worth -128

The 8-bit two's complement place values. The leftmost bit (the sign bit) is worth -128 when it is 1, and the other seven bits keep their usual values, so 10000000 = -128.

Part of: IGCSE Computer Science 0478 — 1.1 Number Systems — Module 29

Understanding The sign bit worth -128 in IGCSE Computer Science Paper 1

What it does: The leftmost 1 adds -128. The other 1s are 64 and 1, which keep their usual values, giving -63. A 0 in the -128 place adds nothing. The remaining bits are added as usual, so the result is positive. The leftmost bit is the sign bit. Its place value is -128, not +128. The leftmost 1 adds -128 and all seven 0s add nothing, so the total is -128. Only the leftmost bit changes to -128. The rest are worked out as normal. Add -128 + 1 = -127. The 1 on the right is worth +1, so it is not -1.

Common mistakes: In 8-bit two's complement the leftmost bit is worth -128, not +128. The line should be sign ← -128, so the answer is -128 + 1 = -127. The other seven bits of 10000000 are all 0, so they add nothing. The total is just the sign bit's value, so the line should be total ← sign, giving -128.

Class: _____________________  ·  Name: _____________________  ·  Date: _________

Free printable worksheet with full answer key — or add this module to a class and your students practise it interactively.

🖨 Print worksheet + answer key Add The sign bit worth -128 to a class →

This module's key terms are also in a printable crossword (Modules 28–41) and word search (Modules 28–58).

Take this worksheet further — free with Cloodit

Each concept is reinforced from every angle — learned, then applied, then tested.

Learning
Duo
In 8-bit two's complement, what is the place value of the leftmost bit?
128-128
Matches
10000001 = 128 + 1 = 129
↓
The leftmost bit was treated as +128. In two's complement it is worth -128, so the answer is -128 + 1 = -127.
Applying
Meanings
Term
-128 64 32 16 8 4 2 1
Meaning
The 8-bit two's complement place values. The leftmost bit (the sign bit) is worth -128 when it is 1, and the other seven bits keep their usual values, so 10000000 = -128.
Practice
place values: -128 64 32 16 8 4 2 1
Testing
Gaps
Place values: 64 32 16 8 4 2 1
Check Answer
Spots
1bits ← 10000001
2sign ← 128

Cloodit turns curriculum-aligned coding content into journeys students work through one biome at a time.

The 'Sand Cat' badge — Precision Prowler, one of Cloodit's 106 collectible badges
Students earn collectable badges

Over 100 of them, across seven natural biomes.

Study Buddy
Students build a real study resource

Turns their work into revision material ready for Flash Cards and Exam study.

Diamond Dash — one of Cloodit's live, competitive Sprint games
Students lock in with Sprints

Live, competitive practice for the start of the lesson or a teacher-led lesson finisher.

A Cloodit certificate of achievement, ready to personalise and print
Custom printable certificates

Honour your top performers, or encourage a student who's trying hard — ready to print in seconds.

Add to class →

Quick Questions

1. In 8-bit two's complement, what is the place value of the leftmost bit?
A. -128 ✓
B. 128
The leftmost bit is the sign bit. Its place value is -128, not +128.
2. Which row shows the 8-bit two's complement place values?
A. -128 -64 -32 -16 -8 -4 -2 -1
B. -128 64 32 16 8 4 2 1 ✓
Only the leftmost place value is negative. The other seven keep their usual positive values.
3. What does the binary pattern 10000000 represent in 8-bit two's complement?
A. -128 ✓
B. 128
The leftmost 1 adds -128 and all seven 0s add nothing, so the total is -128.
4. What happens to the other seven bits in 8-bit two's complement?
A. They keep their usual values: 64, 32, 16, 8, 4, 2, 1 ✓
B. They all become negative
Only the leftmost bit changes to -128. The rest are worked out as normal.
5. What is 10000001 in 8-bit two's complement?
A. -1
B. -127 ✓
Add -128 + 1 = -127. The 1 on the right is worth +1, so it is not -1.

Match the Pairs

-128 64 32 16 8 4 2 1 → The place values of an 8-bit two's complement number, where the leftmost bit is worth -128
10000000 → -128, the smallest 8-bit two's complement number, because only the -128 bit is 1
When the leftmost bit is 1, add -128, then add the usual values of any other bits that are 1 → 11000001 = -128 + 64 + 1 = -63
When the leftmost bit is 0, it adds nothing, so the number is positive and is read like normal binary → 01000001 = 0 + 64 + 1 = 65
10000001 = 128 + 1 = 129 → The leftmost bit was treated as +128. In two's complement it is worth -128, so the answer is -128 + 1 = -127.
10000000 = -128 + 64 = -64 → The 64 was added even though its bit is 0. Only bits that are 1 add their value, so 10000000 = -128.

Key Term

-128 64 32 16 8 4 2 1
The 8-bit two's complement place values. The leftmost bit (the sign bit) is worth -128 when it is 1, and the other seven bits keep their usual values, so 10000000 = -128.

Fill in the Blanks

1. Place values: -128 64 32 16 8 4 2 1
Hint: Type the value of the leftmost bit (the sign bit) in 8-bit two's complement.
2. 10000000 = -128
Hint: Type the 8-bit pattern where only the sign bit is 1 and every other bit is 0.
3. 10000001 = -128 + 1 = -127
Hint: Type the value of the rightmost bit, which keeps its usual place value.
4. 11111111 = -128 + 127 = -1
Hint: Add the sign bit's value to the total of the other seven bits and type the result.
5. 01000000 = 0 + 64 = 64
Hint: The sign bit is 0, so type the usual place value of the second bit from the left.

Spot the Error

Question 1
A bits ← 10000001
B sign ← 128
C rest ← 1
D OUTPUT sign + rest
Line B — In 8-bit two's complement the leftmost bit is worth -128, not +128. The line should be sign ← -128, so the answer is -128 + 1 = -127.
Question 2
A bits ← 10000000
B sign ← -128
C total ← sign + 127
D OUTPUT total
Line C — The other seven bits of 10000000 are all 0, so they add nothing. The total is just the sign bit's value, so the line should be total ← sign, giving -128.
Question 3
A bits ← 11000000
B sign ← -128
C rest ← 64
D total ← sign - rest
Line D — The other bits keep their usual positive values and are added to -128. It should be total ← sign + rest, giving -128 + 64 = -64.
Question 4
A places ← 128 64 32 16 8 4 2 1
B FOR each bit that is 1
C add its place value
Line A — The place values for 8-bit two's complement start with -128. The leftmost value must be -128, not 128.
Question 5
A bits ← 10000100
B total ← -127
C total ← total + 4
D OUTPUT total
Line B — A 1 in the leftmost bit adds -128, not -127. The line should be total ← -128, so the answer is -128 + 4 = -124.

Student with a class code? Join your class →