Question

Convert the following to Octal, hexadecimal and binary (long method (multiply and Divide by methods))

2647.95 (10)

Answer 1

Given decimal number: 2647.95

Decimal to Octal:

converting integer part to octal

	Result	Remainder
8	2647
8	330	7
8	41	2
8	5	1
8	0	5

(2647)₁₀ = (5127)₈

converting fractional part to octal

	product	product	integer part
8	0.95	8*0.95 = 7.6	7
8	0.6	8*0.6 = 4.8	4
8	0.8	8*0.8 = 6.4	6
8	0.4	8*0.4 = 3.2	3
8	0.2	8*0.2 = 1.6	1
8	0.6	8*0.6 = 4.8	4
8	0.8	8*0.8 = 6.4	6
8	0.4	8*0.4 = 3.2	3
8	0.2	8*0.2 = 1.6	1

the same will repeat endless

(0.95)₁₀ = (0.7463146314631463)₈

so (2647.95)₁₀ = (5127.74631463146314631463)₈

Decimal to Hexadecimal:

converting integer part to hexadecimal

	Result	Remainder	Remainder in hex
16	2647
16	165	7	7
16	10	5	5
	0	10	A

(2647)₁₀ = (A57)₁₆

converting fractional part to hexadecimal

	product	product	integer part	hex number
16	0.95	16*0.95 = 15.2	15	F
16	0.2	16*0.2 = 3.2	3	3
16	0.2	16*0.2 = 3.2	3	3
16	0.2	16*0.2 = 3.2	3	3

the same will repeat endless

(0.95)₁₀ = (0.F333333)16

so (2647.95)₁₀ = (A57.F3333333333)16

Decimal to Binary:

converting integer part to binary

	Result	Remainder
2	2647
2	1323	1
2	661	1
2	330	1
2	165	0
2	82	1
2	41	0
2	20	1
2	10	0
2	5	0
2	2	1
2	1	0

(2647)₁₀ = (101001010111)₂

convert fractional part to binary:

	product	product	integer part
2	0.95	2*0.95 = 1.9	1
2	0.9	2*0.9 = 1.8	1
2	0.8	2*0.8 = 1.6	1
2	0.6	2*0.6 = 1.2	1
2	0.2	2*0.2 = 0.4	0
2	0.4	2*0.4 = 0.8	0
2	0.8	2*0.8 = 1.6	1
2	0.6	2*0.6 = 1.2	1
2	0.2	2*0.2 = 0.4	0
2	0.4	2*0.4 = 0.8	0
2	0.8	2*0.8 = 1.6	1
2	0.6	2*0.6 = 1.2	1

the same will repeat endless

(0.95)₁₀ = (0.111100110011)₂

so (2647.95)₁₀ = (101001010111.111100110011)₂