Number System Conversion

Number System Conversion

Here we only focus on the conversion of decimal, binary and hexadecimal.

Figure below show the Decimal/Hexadecimal/Binary Conversion

Decimal to binary

Convert 156₁₀ to binary

2|156    0

2|78      0

2|39      1                      

2|19      1

2|9         1

2|4         0

2|2         0

2|1         1

And we read the answer from the bottom to top, therefore 156₁₀ in binary is 10011100_2.

Decimal to hexadecimal

Convert 1432₁₀ to hexadecimal

Weight	163	162	161	160
Value represented	4096	256	16	1
Hexadecimal		5	9	8

1432 – (256x5) = 152

152 – (16x9) = 8

8 – (1x8) = 0

Therefore 1432₁₀ = 598₁₆

Binary to hexadecimal

Convert 11110000.0011₂ to hexadecimal

1111	0000	.	0011
8421	8421	.	8421
1(8) +1(4) +1(2) +1(1) = 15(F)	0(8) +0(4) +0(2) +0(1) = 0	.	0(8) +0(4) +1(2) +1(1) = 3

11110000.0011₂ = F0.3₁₆

Hexadecimal to binary

E186₁₆ = ?

E	1	8	6
1110	0001	1000	0110

Therefore E186₁₆ = 1110000110000110₂

Binary to hexadecimal

11010₂ = ?

Binary	1	1	0	1	0
Weight	24	23	22	21	20
Value	16	8	4	2	1

11010₂ = 1(16) + 1(8) + 0(4) + 1(2) + 0(1)

                = 26

by: Muhammad Nasruddin Rosli

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Muted Professor

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