Rules of Thumb

Rule 1

Binary to Hex Conversion

Rule 2

Place Values of Binary Bits 0 to 7

Bit 07	Bit 06	Bit 05	Bit 04	Bit 03	Bit 02	Bit 01	Bit 00
128	64	32	16	8	4	2	1

Place Values of Binary Bits 8 to 15

Bit 15	Bit 14	Bit 13	Bit 12	Bit 11	Bit 10	Bit 09	Bit 08
32768	16384	8192	4096	2048	1024	512	256

Rule 3

Magic Numbers which you will need to remember:

1kiloByte	1MegaByte	1GigaByte
1,024byte	1024x1024byte	1024x1024x1024byte
10 bits wide	20 bits wide	30 bits wide

Rule 4

Binary Fractions Conversions

Point (.)	Bit 1	Bit 2	Bit 3	Bit 4	Bit 5	Bit 6
Fraction	1/2	1/4	1/8	1/16	1/32	1/64
Binary	0.1	0.01	0.001	0.0001	0.00001	0.000001
Decimal	0.5	0.25	0.125	0.0625	0.03125	0.015625

Note: Number of Binary Places = Number of Decimal Places

Rule 5

Denary to Binary using Boggle Method

Convert Denary 27 to Binary
1	3	6	13	27
1	1	0	1	1

Start at the right hand side and write down half the value of the starting number to the left. If there is a remainder, ignor it and round the number down to the next integer. Keep halving and moving left until you end up with a one (1). Now under each number in the list, put a one (1) under any odd numbers and a zero (0) under any even numbers. Read off the Binary Number created.

Here is a second example:

Convert Denary 51 to Binary
1	3	6	12	25	51
1	1	0	0	1	1

And here is another:

Convert Denary 72 to Binary
1	2	4	9	18	36	72
1	0	0	1	0	0	0

Rule 6

Binary to Denary using Boggle Method

Convert Binary 1001000 to Denary
1	0	0	1	0	0	0
1	2	4	9	18	36	72

Start at the left hand side and put a one (1) beneath the first Binary Digit. Now double it and add to the next Binary Digit to the right and write this down in the next column. Continue doubling the number and adding the next Binary Digit until there are no nore left. The final number is the result.

Here is a second example:

Convert Binary 110101 to Denary
1	1	0	1	0	1
1	3	6	13	26	53

Rule 7

IEEE 754 Single Precision Number Format

This number format is used as the internal representation of real numbers within the computer. It consistes of three parts, Sign, Exponent, Mantissa, which are assembled as follows:

Convert -111.28125 to IEEE 754 format:

Sign = negative, bit 1 = 1

Integer 111 (using Boggle) = 1101111

Boggle 111
1	3	6	13	27	55	111
1	1	0	1	1	1	1

Fraction is 5 bits long (n/32) so 32 x 0.28125 = 9 (9/32) = 0.01001

Re-assemble number = 1101111.01001

Normalise = 1.10111101001 x 10⁶

Exponent = 6 + 127 = 133 = 10000101 using Boggle

Boggle 133
1	2	4	8	16	33	66	133
1	0	0	0	0	1	0	1

Now bring all the parts together. Note: The leading 1 and the point from mantissa are no longer required in the number.

Sign	Exponent	Mantissa
1	10000101	10111101001

Now block out in 4 bit groups and convert to hex. Add extra 4 bit groups to bring up to 32 bits total length.

IEEE754 Format
1100	0010	1101	1110	1001	0000	0000	0000
C	2	D	E	9	0	0	0

Final Answer: -111.28125 = C2DE 9000

Rule 8

Screen Resolutions all stem from a common ratio of 1.25:1 which gives rise to the common series of resolutions as shown:

Screen Resolutions
Width	320	640	800	1024	1280	1600
Height	240	480	600	768	1024	1280

Rule 9

Colours are displayed on the screen by using varying amounts of the three Primary Additive Colours: Red, Blue and Green. By mixing these three colours in differing amounts, all the colours can be produced. The colours are stored in the video RAM as numbers and the three primary colours each have their own set of bits. The number of bits available gives the total number of colours that it is possible to display. Each Pixel (Picture Element) on the screen requires all the bits for each colour. So the total amount of memory required for a video display is X Pixels x Y Pixels x Colour Depth. Common values for colour depth are:

Screen Colours
Bits	(4+4+4) = 12	(6+6+6) = 18	(8+8+8) = 24	(10+10+10) = 30
Colours	16, 64, 256 1	65K or 250k	16M	True Colour 2

Note:
1. Although 12 bits allows 4096 colours, this bit pattern was used historically to support EGA which had 8 light and 8 dark colours used as text forground and background colours. The pallet also supported blinking colours and graphical fonts which also reduced the number of colours available. The common colour depths are now 16, 64 and 256 colours only.
2. True Colour is usually defined as 32 bit colour but once again the extra two bits are control bits and play no part in colour rendering. When displaying games some extra bits are used to overlay texture maps for complex surfaces and some video cards use the extra bits to control screen buffering (where more than one frame is set up in RAM and the display is toggled back and forth between the two).