Binary Number System

• A Base 2 number system
• There are 2 symbols that represent quantities,
• 0 and 1
• Each place value in a binary number is a power of 2
• 2³, 2², 2¹, 2⁰
• 57₁₀ to binary

 

• Convert 0.437510to binary

     Convert 1100111₂ to Decimal

26	25	24	23	22	21	20
1	1	0	0	1	1	1
64	32	16	8	4	2	1

• 1100111₂=2⁶x1+2⁵x1+2⁴x0+2³x0+2²  x1+2¹x1+2⁰x1
• 1100111₂=64₁₀+32₁₀+4₁₀+2₁₀+1₁₀
• 1100111₂=103₁₀  

Convert 0.11011₂ to Decimal

2-1	2-2	2-3	2-4	2-5
1	1	0	1	1
64	32	16	8	4

•            0.11011₂=2^-1x1+2^-2x1+2^-3x0+2^-4x1+2^-5x1
•            0.11011₂=0.5₁₀+0.25₁₀+0.0625₁₀+0.03125₁₀
•      0.11011₂=0.84375₁₀