Which of the following statements about data types is wrong?

Concept

A data type's storage is a fixed number of bits, and that width fixes the total count of distinct values it can hold (2^n for n bits). 'signed' versus 'unsigned' does not change how many values exist — it only changes which values those bit-patterns are mapped to. A signed type dedicates one bit to recording the sign, so its patterns are split between negative and non-negative numbers; an unsigned type uses every bit for magnitude, so all its patterns are non-negative.

Applying it to each statement

Read every statement and decide whether it is true; the question asks for the one that is wrong.

• Unsigned removes the sign, so it cannot store a negative number (it stores non-negative values) — a true description of unsigned behaviour.

• Signed reserves a sign bit, so it can store both negative and non-negative numbers — a true description of signed behaviour.

• Signed has a greater range than unsigned — this is the claim to test below.

• In unsigned, no bit is reserved for a sign, so every bit (including the leftmost) carries magnitude — a true description.

Cross-check the range claim with an 8-bit example

1. Unsigned 8-bit uses all 8 bits for magnitude: it covers 0 to 255, so its maximum value is 255.

2. Signed 8-bit (two's complement) spends one bit on the sign: it covers -128 to 127, so its maximum value is 127.

3. Both hold 2^8 = 256 distinct values, but the unsigned maximum (255) is larger than the signed maximum (127).

Result

Because the unsigned type reaches a higher maximum value for the same width, the statement claiming that signed types have a larger range than unsigned types does not hold. The other three statements correctly describe how signed and unsigned types behave.