How to convert positive denary whole numbers to binary numbers (up to and including 8 bits) and vice versa

Numbers: How to convert positive denary whole numbers to binary numbers (up to and including 8 bits) and vice versa

1.2.4a Data Storage: Numbers

Data Storage: Numbers — Note 1 of 5

What you need to know

Denary (decimal, base 10) numbers need to be converted to binary (base 2) for computer processing. You must be able to convert both ways for numbers 0-255 using up to 8 bits.

What to know

Binary uses place value headers based on powers of 2: 128, 64, 32, 16, 8, 4, 2, 1.
Adding leading zeros does not change the value: 11010 = 00011010.

Key terms

Exam tipCommon mistake

DenaryBase 10: A number system that uses ten digits, from 0 to 9.
To convert binary to denary: add together the place values where there is a 1.
To convert denary to binary: start from the largest place value, place a 1 if it fits (subtract it), 0 if not, then move right.
Exam tip: The largest denary number in n bits = 2^n - 1. E.g. 6 bits = 63 (not 64). 8 bits = 255 (not 256).
Most Significant BitMSB: The leftmost 1 in a binary number — it has the highest value.
Least Significant BitLSB: The rightmost bit — it has the lowest value (1).

Exam technique

Tip:Always write out the place value headers (128, 64, 32, 16, 8, 4, 2, 1) when doing conversions — it reduces mistakes.
Tip:If the answer must be 8-bit binary, you MUST include leading zeros. '111' must be written as 00000111.
Mistake:Writing the binary header numbers the wrong way around (1, 2, 4, 8... left-to-right). The LEFTMOST bit must be the HIGHEST value (128).
Mistake:Saying the smallest number in 4-bit binary is 1. It is 0 (0000). The smallest is always 0.

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