Representation

• Terminology

  • least significant bit (lsb): least magnitude bit.
  • most significant bit (msb): greatest magnitude bit.
  • unsigned integers: k bit sequence representing 0 to 2k-1
  • two's complement: number representation for signed integers.

Unsigned Binary Decimal 2s Complement Binary Decimal

0000 0000 0000 0000 0 0000 0000 0000 0000 0

0000 0000 0000 0001 1 0000 0000 0000 0001 1

0000 0000 0000 0010 2 0000 0000 0000 0010 2

. . . . . .

1111 1111 1111 1101 65533 0111 1111 1111 1111 32767

1111 1111 1111 1110 65534 1000 0000 0000 0000 -32768

1111 1111 1111 1111 65535 1000 0000 0000 0001 -32767

1000 0000 0000 0010 -32766

. . .

1111 1111 1111 1101 -3

1111 1111 1111 1110 -2

1111 1111 1111 1111 -1

2s Complement

is “unbalanced”

since it has 1 more

negative number

than positive

numbers. Why?

Unsigned gets a larger

range at the expense of

no negative representation

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