Worksheet

F8.5 Negative numbers: two's complement

Data representation · GCSE · Edexcel 1CP2 2.1.2 · about 12 min

What this lesson is about

Signed 8-bit integers, and why the same adder works for them.

• The idea
• Making a number negative
• Why it works so well
• Negative speeds

Questions 4 marks in all

1. [1 mark]Write -5 in 8-bit two's complement.

2. [1 mark]What is 11111111 in 8-bit two's complement?

3. [1 mark]What range can an 8-bit two's complement number hold?

   1. A-128 to 127
   2. B-127 to 127
   3. C0 to 255
   4. D-255 to 255

4. [1 mark]What does a leftmost bit of 1 mean in two's complement?

   1. AThe number is negative
   2. BThe number is odd
   3. CThe number is over 100
   4. DOverflow happened

The task: signed readings

Write to_twos(n) yourself for -128 to 127 (you may use format(n, "08b") for the positive part). Print the 8-bit two's complement of 42, -42 and -128, one per line, in the form -42 = 11010110.

# the two lines every program starts with: the commands, then the robot
from bugbot import *
connect()

def to_twos(n):
    return format(n, "08b")

Plan your program here, then type it in and press Run.

Do it on the robot
www.bugbotlab.com/learn/f8-5-twos-complement/
The simulator checks it and tells you when it passes. Nothing to install, no account.

Challenges

1. What happens if you try to_twos(200)? Add a check that refuses numbers out of range.
2. Add -60 and 40 as 8-bit two's complement using the adder from F8.4. Is the answer right?
3. How many bits would a two's complement number need to hold -1,000?