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Answers

F8.5 Negative numbers: two's complement

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

BugBotLab

What this lesson is about

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

Questions 4 marks in all

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

    Answer: 11111011. 5 is 00000101; flip to 11111010; add 1.

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

    Answer: -1. -128 + 127 = -1.

  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
    Answer: A. The leftmost bit is worth -128.

  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
    Answer: A. Only the -128 place can make the total negative.

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")

The hint students can ask for: For a negative n: write -n in 8-bit binary, flip every bit, and add 1.

A solution

from bugbot import *
connect()
def to_twos(n):
    if n >= 0:
        return format(n, "08b")
    flipped = ""
    for bit in format(-n, "08b"):
        flipped = flipped + ("0" if bit == "1" else "1")
    return format(int(flipped, 2) + 1, "08b")

for n in [42, -42, -128]:
    print(n, "=", to_twos(n))

Any program that meets the task's checks is marked correct in the simulator; this is one way, not the only way.