Transfer 2B3C4F.5 from hexadecimal in binary number system

This transfer is possible in two ways: direct transfer and using the decimal system.

first, let\'s make a direct transfer.

let\'s do a direct translation from hexadecimal to binary like this:

2B3C4F.5₁₆ = 2 B 3 C 4 F. 5 = 2_(=0010) B_(=1011) 3_(=0011) C_(=1100) 4_(=0100) F_(=1111). 5_(=0101) = 1010110011110001001111.0101₂

the Final answer: 2B3C4F.5₁₆ = 1010110011110001001111.0101₂

now let\'s make the transfer using the decimal system.

let\'s translate to decimal like this:

2∙16⁵+11∙16⁴+3∙16³+12∙16²+4∙16¹+15∙16⁰+5∙16^-1 = 2∙1048576+11∙65536+3∙4096+12∙256+4∙16+15∙1+5∙0.0625 = 2097152+720896+12288+3072+64+15+0.3125 = 2833487.3125₁₀

got It: 2B3C4F.5₁₆ =2833487.3125₁₀

Translate the number 2833487.3125₁₀ в binary like this:

the Integer part of the number is divided by the base of the new number system:

2833487	2
-2833486	1416743	2
1	-1416742	708371	2
	1	-708370	354185	2
		1	-354184	177092	2
			1	-177092	88546	2
				0	-88546	44273	2
					0	-44272	22136	2
						1	-22136	11068	2
							0	-11068	5534	2
								0	-5534	2767	2
									0	-2766	1383	2
										1	-1382	691	2
											1	-690	345	2
												1	-344	172	2
													1	-172	86	2
														0	-86	43	2
															0	-42	21	2
																1	-20	10	2
																	1	-10	5	2
																		0	-4	2	2
																			1	-2	1
																				0