Information Representation

//Two's complement, and why it is clever

To make a number negative: invert every bit, then add 1. The leftmost bit becomes the sign bit — 1 means negative. The beauty is that subtraction becomes addition, so the processor needs only one circuit.

 5  = 0000 0101
invert  1111 1010
add 1   1111 1011  = -5

8 - 5 is done as 8 + (-5):
   0000 1000
 + 1111 1011
 ------------
 1 0000 0011      carry off the end is discarded
                  answer 0000 0011 = 3

//Range of an 8-bit two's complement number

One bit is the sign, so the range is −128 to +127. Note it is not symmetrical — there is one more negative value than positive, because zero takes a positive slot.

//BCD, and where it is used

Each denary digit is stored in its own 4 bits, so 59 is 0101 1001. It wastes space and is awkward for arithmetic, but converting to a display is trivial — which is why it is used in digital clocks, calculators and money systems where exact decimal values matter.

//Bitmap vs vector

Bitmap stores every pixel, so it handles photographs but becomes blocky when enlarged and the file grows with resolution. Vector stores shapes as instructions, so it scales to any size with no loss and stays small — but it cannot represent a photograph.

KEY TERMS

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