Mathematics Basic Skills

Addition

What is addition?

Addition is a way to put things together. When you add two amounts, you're counting them together, as one larger amount. Addition happens all the time in real life.

Number Systems

Binary to Decimal Conversion

Conversion of binary to decimal (base-2 to base-10) numbers and back is an important concept to understand as the binary numbering system forms the basis for all computer and digital systems.

Examples:

10101₂ = 10101B = 1×2⁴+0×2³+1×2²+0×2¹+1×2⁰ = 16+4+1= 2110111₂ = 10111B = 1×2⁴+0×2³+1×2²+1×2¹+1×2⁰ = 16+4+2+1= 23100011₂ = 100011B = 1×2⁵+0×2⁴+0×2³+0×2²+1×2¹+1×2⁰=32+2+1= 35

Summary

• A “BIT” is the abbreviated term derived from BInary digiT
• A Binary system has only two states, Logic “0” and Logic “1” giving a base of 2
• A Decimal system uses 10 different digits, 0 to 9 giving it a base of 10
• A Binary number is a weighted number who’s weighted value increases from right to left
• The weight of a binary digit doubles from right to left
• A decimal number can be converted to a binary number by using the sum-of-weights method or the repeated division-by-2 method
• When we convert numbers from binary to decimal, or decimal to binary, subscripts are used to avoid errors