Worksheet

F8.4 Binary addition, overflow and shifts

Data representation · GCSE · OCR J277 1.2.4, AQA 8525 3.3.4, Edexcel 1CP2 2.1.4 · about 15 min

What this lesson is about

Adding in binary with carries, overflow, and shifting to multiply and divide.

• Adding binary
• Overflow
• Shifts

Questions 5 marks in all

1. [1 mark]Add 01011010 and 00110111 in binary.

2. [1 mark]What is overflow?

   1. AA result too large to fit in the number of bits available
   2. BA number with too many decimal places
   3. CRunning out of memory for files
   4. DA loop that never ends

3. [1 mark]In 8 bits, 200 + 100 overflows. What value do the 8 bits kept hold?

4. [1 mark]What does this program print?

   print(13 << 1, 13 << 2, 13 >> 1)

5. [1 mark]What does shifting a binary number two places left do?

   1. AMultiplies it by 4
   2. BMultiplies it by 2
   3. CDivides it by 4
   4. DAdds 2

The task: an 8-bit adder

Write add_binary(a, b) yourself (no int(..., 2) or bin inside it) that adds two 8-bit strings and returns the 8-bit answer and the carry out. Print 01011010 + 00110111 = 10010001 and, on the next line, 11001000 + 01100100 = 00101100 overflow, working both answers out with your function.

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

def add_binary(a, b):
    return "00000000", 0

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

Do it on the robot
www.bugbotlab.com/learn/f8-4-binary-addition-overflow-and-shifts/
The simulator checks it and tells you when it passes. Nothing to install, no account.

Challenges

1. Add three 8-bit numbers with your function, and check when overflow happens.
2. Write shift_left(bits) on strings: drop the first character and add a 0 at the end. Check it doubles the number.
3. Why does shifting right lose information? Find a number that shifting right then left does not bring back.