State the range of denary values that can be represented using 8‑bit two’s complement.

1. Calculate how many values can be stored with 8 bits
2^8 = 256

2. Half of the values will be positive and half will be negative
256 / 2 = 128

3. Answer
-128 to 127

(NOTE: Zero counts as a positive number so you need to remove 1 from the positive end of the range.)

The formula to calculate the range of numbers that can be represented using two’s complement is:

-2^(n-1)    to    2^(n-1) – 1

Example:
State the range of denary values that can be represented using 8‑bit two’s complement.

-2^(n-1)    to    2^(n-1) – 1
-2^(8-1)    to    2^(8-1) – 1
-2^(7)    to    2^(7) – 1
-128    to   128 – 1
-128    to   127