H Plenary - Two's complement and range of numbers

Binary conversion questions will always be negative numbers at higher level.

• True

• False

Answer explanation

Any simple binary conversion question in the higher computing science paper will involve the conversion of negative numbers only.

Reorder the following steps for converting negative denary numbers into binary.

• Add 1 to the number

• Represent the positive number in binary

• Change 1's to 0's and vice versa

Convert the following denary number to an 8‑bit two’s complement number.

−25

Answer explanation

The steps involved in answering this question would be as follows.

Represent the positive number in binary =

00011001

Swap the 1's and 0's =

11100110

Add 1 to the number =

11100111

State the largest positive integer that can be represented using 8‑bit two’s complement.

Answer explanation

The largest positive number with 8 bits would be 64 + 32 + 16 + 8 + 4 + 2 + 1 = 127

Convert the 8-bit two’s complement number 1111 0000 into denary.

Answer explanation

(-128) + 64 + 32 + 16 = -16