Integers and two's complement

Unsigned and signed integers on 8, 16 and 32 bits: representable range, sign and magnitude, one's complement, two's complement and sign extension.

The outline, topic by topic

Each topic is weighted the way the exam weighs it.

Unsigned integer: what is it?
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An integer coded on n bits that only represents positive values or zero, from 0 to 2ⁿ − 1.
On 8 bits: 0 to 255. All 256 patterns stand for non-negative values, and no negative value exists.
On 8 bits, what is the pattern of −5 in two's complement?
- 1111 1011
- 1111 1010
- 1000 0101
- 0000 0101
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1111 1011
5 = 0000 0101, flipped 1111 1010, plus 1: 1111 1011. 1111 1010 is one's complement, 1000 0101 is sign and magnitude, 0000 0101 is +5.
To get the negation of an integer in two's complement, … all its bits then ….
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To get the negation of an integer in two's complement, flip all its bits then add 1.
Flipping alone gives one's complement, which is off by 1: −1 would then be 1111 1110 instead of 1111 1111.
Two's complement: what is it?
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A signed integer encoding in which the negation of a number is obtained by flipping all its bits then adding 1.
−42 on 8 bits: 42 = 0010 1010, flipped 1101 0101, plus 1: 1101 0110. Advantage: adding signed integers uses the same circuit as unsigned ones.