Hexadecimal fractions to decimal numbers

This post is explain how to convert hexadecimal fractions to decimal numbers. As we known, hexadecimal number is system number who have 16 digit numbers, which is 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E and F, where:
A present of 10
B present of 11
C present of 12
D present of 13
E present of 14
F present of 15.

The picture below is show hexadecimal fraction to decimal, form 1st position to 5th position of the digit, before and after the hexadecimal point.

Hexadecimal fractions to decimal

Example 1:
Convert hexadecimal number 0.59A to decimal number

Completion:
0.59A ₍₁₆₎ = ... ₍₁₀₎
1st digit after hexadecimal point: 5 → 5 × (1/ 16¹) = 5 × 0.0625 = 0.3125
2nd digit after hexadecimal point: 9 → 9 × (1/ 16²) = 9 × 0.00390625 = 0.03515625
3rd digit after hexadecimal point: A → 10 × (1/ 16³) = 10 × 0.000244141 = 0.00244141
sum all → 0.3125 + 0.03515625 + 0.00244141 = 0.35009766

0.59A ₍₁₆₎ = 0.35009766 ₍₁₀₎

Example 2:
Convert hexadecimal number E2.81AC to decimal number

Completion:
E2.81AC ₍₁₆₎ = ... ₍₁₀₎

before hexadecimal point
1st digit: 2 → 2 × 16⁰ = 2 × 1 = 2
2nd digit: E → 14 × 16¹ = 14 × 16 = 224
sum all → 2 + 224 = 226

after hexadecimal point
1st digit: 8 → 8 × (1/ 16¹) = 8 × 0.0625 = 0.5
2nd digit: 1 → 1 × (1/ 16²) = 1 × 0.00390625 = 0.00390625
3rd digit: A → 10 × (1/ 16³) = 10 × 0.000244141 = 0.00244141
4th digit: C → 12 × (1/ 16⁴) = 12 × 0.000015259 = 0.000183108
sum all → 0.5 + 0.00390625 + 0.00244141 + 0.000183108 = 0.506530768

E2.81AC ₍₁₆₎ = 226.506530768 ₍₁₀₎

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Table of the electric currents of a 3-phase motor

An electric motor has specifications: voltage is 380 V, 3 phase, frequency is 50 Hz, 1500 rpm, cos phi is 0.8 and real power on the name plate is 22 kW. Convert to HP (Horse Power) and calculate, how many current of electricity will flow into the motor?

Connection of 3-Phase Motor

:catat: Answer:
1HP = 0.75 kW --> 22 kW / 0.75 kW x 1 HP = 29.33 HP
--> 22 kW ≈ 30 HP
:catat: The power of the motor is 30 HP

V = 380 V 3 fase
f = 50 Hz
Cos φ = 0.8
P = 22 kW = 22000 W
I = ...?

The formula of real power electricity in 3-phase:
P = √3 x V x I x Cos φ --> I = P / (√3 x V x Cos φ)
--> I = 22000 / (√3 x 380 x 0.8)
--> I = 41.78 A
:catat: The current of electricity will flow into the motor is 41,78 A

For reference, here is a table of the electric currents of a 3-phase motor, 380 V, cos phi 0.8

kW	HP	A
0.4	0.5	0.8
0.75	1	1.4
1.1	1.5	2.1
1.5	2	2.8
2.2	3	4.2
3	4	5.7
3.7	5	7
4.5	6	8.5
5.5	7.5	10.4
7.5	10	14.2
9	12	17.1
11	15	20.9
15	20	28.5
18.5	25	35.1
22	30	41.8
30	40	57
37	50	70.3
45	60	85.5
55	75	104.5
75	100	142.4

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Octal fractions to decimal numbers

This post is explain how to convert octal fractions to decimal numbers. The picture below is show octal fraction to decimal, form 1st position to 5th position of the digit, before and after the octal point.

Octal fractions to decimal

Example 1:
Convert Octal number 0.725 to decimal number

Completion:
0.725 ₍₈₎ = ... ₍₁₀₎
1st digit after octal point: 7 → 7 × (1/ 8¹) = 7 × 0.125 = 0.875
2nd digit after octal point: 2 → 2 × (1/ 8²) = 2 × 0.015625 = 0.03125
3rd digit after octal point: 5 → 5 × (1/ 8³) = 5 × 0.001953125 = 0.009765625
sum all → 0.875 + 0.03125 + 0.009765625 = 0.916015625

0.725 ₍₈₎ = 0.916015625 ₍₁₀₎

Example 2:
Convert octal number 105.2063 to decimal number

Completion:
105.2063 ₍₈₎ = ... ₍₁₀₎

before octal point
1st digit: 5 → 5 × 8⁰ = 5 × 1 = 5
2nd digit: 0 → 0 × 8¹ = 0 × 8 = 0
3rd digit: 1 → 1 × 8² = 1 × 64 = 64
sum all → 5 + 0 + 64 = 69

after octal point
1st digit: 2 → 2 × (1/ 8¹) = 2 × 0.125 = 0.25
2nd digit: 0 → 0 × (1/ 8²) = 0 × 0.015625 = 0
3rd digit: 6 → 6 × (1/ 8³) = 6 × 0.001953125 = 0.01171875
4th digit: 3 → 3 × (1/ 8⁴) = 3 × 0.000244141 = 0.000732423
sum all → 0.25 + 0 + 0.01171875 + 0.000732423 = 0.262451173

501.2063 ₍₈₎ = 69.262451173 ₍₁₀₎

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Binary fractions to decimal numbers

This post is explain how to convert binary fractions to decimal numbers. The picture below is show binary fraction to decimal, form 1st position to 5th position of the digit, before and after the binary point.

Binary fractions to decimal

Example 1:
Convert binary number 0.1101 to decimal number

Completion:
0.101 ₍₂₎ = ... ₍₁₀₎
1st digit after binary point: 1 → 1 × (1/ 2¹) = 1 × 0.5 = 0.5
2nd digit after binary point: 0 → 0 × (1/ 2²) = 0 × 0.25 = 0
3rd digit after binary point: 1 → 1 × (1/ 2³) = 1 × 0.125 = 0.125
sum all → 0.5 + 0 + 0.125 = 0.625

0.101 ₍₂₎ = 0.625 ₍₁₀₎

Example 2:
Convert binary number 1110.11011 to decimal number

Completion:
1110.11011 ₍₂₎ = ... ₍₁₀₎

before binary point
1st digit: 0 → 1 × 2⁰ = 0 × 1 = 0
2nd digit: 1 → 1 × 2¹ = 1 × 2 = 2
3rd digit: 1 → 1 × 2² = 1 × 4 = 4
4th digit: 1 → 1 × 2³ = 1 × 8 = 8
sum all → 0 + 2 + 4 + 8 = 14

after binary point
1st digit: 1 → 1 × (1/ 2¹) = 1 × 0.5 = 0.5
2nd digit: 1 → 1 × (1/ 2²) = 1 × 0.25 = 0.25
3rd digit: 0 → 0 × (1/ 2³) = 0 × 0.125 = 0
4th digit: 1 → 1 × (1/ 2⁴) = 1 × 0.0625 = 0.0625
5th digit: 1 → 1 × (1/ 2⁵) = 1 × 0.03125 = 0.03125
sum all → 0.5 + 0.25 + 0 + 0.0625 + 0.03125 = 0.84375

1110.11011 ₍₂₎ = 14.84375 ₍₁₀₎

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How to calculate current motor value in single phase motor?

:1: There is an electric motor that used to drive conveyor machine. The electric motor has specifications: voltage is 200 Volt single phase, frequency is 50 Hz, cos phi is 0.82 and real power on the name plate is 330 Watt. How many current of electricity will flow into the motor?

:catat: Answer:
V = 200 Volt
f = 50 Hz
Cos phi = 0.82
P = 330 W
I = ...?

===================================
The formula of real power electricity in single phase motor
P = V I Cos phi . . . . . (Watt)

:pin: then

The formula of current electricity in single phase motor
I = P / (V Cos phi) . . . . . (Ampere)
====================================

I = 330 / (200 * 0.82)
I = 2 A.

:2: In the chocolate factory has an electric motor that has specifications: voltage is 220 Volt single phase, frequency is 50 Hz, cos phi is 0.78 and real power on the name plate is 2.2 kW. How many current of electricity will flow into the motor?

:catat: Answer:
V = 220 Volt
f = 50 Hz
Cos φ = 0.78
P = 2.2 kW → convert kW into W → 2.2 * 10³ W = 2200 W
I = ...?

I = P / (V Cos φ)
I = 2200 / (220 * 0.78)
I = 12.82 A.

:3: The electric motor has specifications: voltage is 400 Volt single phase, frequency is 60 Hz, Cos φ is 0.85 Ampere and real power on the name plate is 6 HP. How many current of electricity will flow into the motor?

:catat: Answer:
V = 400 Volt
f = 60 Hz
Cos φ = 0.85
P = 6 HP → convert HP into W → 6 * 746 W = 4476 W
I = ...?

I = P / (V Cos φ)
I = 4476 / (400 * 0.85)
I = 13.165 A.

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How to calculate cos phi motor value in single phase motor?

:1: We have an electric motor that used to drive washing machine. The electric motor has specifications: voltage is 220 Volt single phase, frequency is 50 Hz, current of electricity is 1.24 Ampere and real power on the name plate is 200 Watt. How many cos phi of electricity of the motor?

:catat: Answer:
V = 220 Volt
f = 50 Hz
I = 1.24 A
P = 200 W
Cos phi = ...?

===================================
The formula of real power electricity in single phase motor
P = V I Cos phi . . . . . (Watt)

then

The formula of cos phi in single phase motor
Cos phi = P / (V I)
or
Cos φ = P / (V I)
====================================

Cos phi = 200 / (220 * 1.24)
Cos phi = 0.733.

:2: In the paper bag factory has an electric motor that has specifications: voltage is 200 Volt single phase, frequency is 60 Hz, current of electricity is 9.5 Ampere and real power on the name plate is 1.5 kW. How many cos φ of electricity of the motor?

:catat: Answer:
V = 200 Volt
f = 60 Hz
I = 9.5 A
P = 1.5 kW → convert kW into W → 1.5 * 10³ W = 1500 W
Cos φ = ...?

Cos φ = P / (V I)
Cos φ = 1500 / (200 * 9.5)
Cos φ = 0.79.

:3: The electric motor has specifications: voltage is 400 Volt single phase, frequency is 70 Hz, current of electricity is 10.97 Ampere and real power on the name plate is 4 HP. How many cos φ of electricity of the motor?

:catat: Answer:
V = 400 Volt
f = 70 Hz
I = 10.97 A
P = 4 HP → convert HP into W → 4 * 746 W = 2984 W
Cos φ = ...?

Cos φ = P / (V I)
Cos φ = 2984 / (400 * 10.97)
Cos φ = 0.68.

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How to calculate power motor value in kW to HP?

:1: There is an electric motor that used to drive water pump machine. The electric motor has specification: voltage 220 Volt single phase, frequency 50 Hz, current 9 Ampere and power 1.2 kW. How many horse power or HP power of electricity that used the motor?

:catat: Answer:
V = 220 Volt
f = 50 Hz
I = 9 A
P = 1.2 kW
P = ...? HP

====================================
The conversion formula of kW to HP
1 kW = 1/ 0.746 HP
=====================================

P = 1.2 / 0.746 HP
P = 1.61 HP.

:2: In the workshop has an electric motor that has specification: voltage 200 Volt single phase, frequency 60 Hz, and power 2.5 HP. How many kilo Watt power of electricity that used the motor?

:catat: Answer:
V = 200 Volt
f = 60 Hz
P = 2.5 HP
P = ...? kW

====================================
The conversion formula of HP to kW
1 HP = 0.746 kW
=====================================

P = 2.5 * 0.746 kW
P = 1.865 kW.

:3: The electric motor has specification: voltage 400 Volt single phase, frequency 70 Hz, current 8.5 Ampere and cos phi 0.75. How many horse power or HP power of electricity that used the motor?

:catat: Answer:
V = 400 Volt
f = 70 Hz
I = 8.5 A
Cos phi = 0.75
P = ...? HP

P = V I Cos phi
P = 400 * 8.5 * 0.75
P = 2550 Watt
P = 2.55 kW
P = 3.418 HP.

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How to calculate power motor value in single phase motor?

:1: We have an electric motor that used to drive fan machine. The electric motor has specification: voltage 220 Volt single phase, frequency 50 Hz, current 0.5 Ampere and cos phi 0.6. How many power of electric that used the motor?

:catat: Answer:
V = 220 Volt
f = 50 Hz
I = 0.5 A
Cos phi = 0.6
P = ... ?

P = V I Cos phi
P = 220 * 0.5 * 0.6
P = 66 Watt.

:2: The electric motor has specification: voltage 110 Volt single phase, frequency 60 Hz, current 3.3 Ampere and cos phi 0.75. How many power of electric that used the motor?

:catat: Answer:
V = 110 Volt
f = 60 Hz
I = 3.3 A
Cos phi = 0.75
P = ... ?

P = V I Cos phi
P = 110 * 3.3 * 0.75
P = 272.25 Watt.

:3: The electric motor has specification: voltage 400 Volt single phase, frequency 70 Hz, current 10 Ampere and cos phi 0.65. How many kilo Watt power of electric that used the motor?

:catat: Answer:
V = 400 Volt
f = 70 Hz
I = 10 A
Cos phi = 0.65
P = ... ?

P = V I Cos phi
P = 400 * 10 * 0.65
P = 2600 Watt
P = 2.6 kW.

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Hexadecimal numbers to octal numbers

Convert hexadecimal numbers to octal numbers
1. F4
2. ADE
3. 8C1F

Completion:
1. F4 ₍₁₆₎ = ? ₍₈₎
* First, convert hexadecimal numbers to decimal numbers. Then, convert decimal numbers to octal numbers.

hexadecimal to decimal
F4 = 4x16⁰ + Fx16¹
F4 = 4x16⁰ + 15x16¹
F4 = 4 + 240
F4 ₍₁₆₎ = 244 ₍₁₀₎

decimal to octal
244 / 8 = 30, remains 4
30 / 8 = 3, remains 6
3 / 8 = 0, remains 3
244 ₍₁₀₎ = 364 ₍₈₎

F4 hexadecimal number equal to 364 octal number
F4 ₍₁₆₎ = 364 ₍₈₎

2. ADE ₍₁₆₎ = ? ₍₈₎
hexadecimal to decimal
ADE = Ex16⁰ + Dx16¹ + Ax16²
ADE = 14x16⁰ + 13x16¹ + 10x16²
ADE = 14 + 208 + 2560
ADE ₍₁₆₎ = 2782 ₍₁₀₎

decimal to octal
2782 / 8 = 347, remains 6
347 / 8 = 43, remains 3
43 / 8 = 5, remains 3
5 / 8 = 0, remains 5
3501 ₍₁₀₎ = 5336 ₍₈₎

ADE hexadecimal number equal to 5336 octal number
ADE ₍₁₆₎ = 5336 ₍₈₎

3. 8C1F ₍₁₆₎ = ? ₍₈₎
hexadecimal to decimal
8C1F = Fx16⁰ + 1x16¹ + Cx16² + 8x16³
8C1F = 15x16⁰ + 1x16¹ + 12x16² + 8x16³
8C1F = 15 + 16 + 3072 + 32768
8C1F ₍₁₆₎ = 35871 ₍₁₀₎

decimal to octal
35871 / 8 = 4483, remains 7
4483 / 8 = 560, remains 3
560 / 8 = 70, remains 0
70 / 8 = 8, remains 6
8 / 8 = 1, remains 0
1 / 8 = 0, remains 1
605025 ₍₁₀₎ = 106037 ₍₈₎

8C1F hexadecimal number equal to 106037 octal number
8C1F ₍₁₆₎ = 106037 ₍₈₎

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Hexadecimal numbers to binary numbers

Convert hexadecimal numbers to binary numbers
1. 2B
2. DAD
3. FE01

Completion:
1. 2B ₍₁₆₎ = ? ₍₂₎
* First, convert hexadecimal numbers to decimal numbers. Then, convert decimal numbers to binary numbers.

hexadecimal to decimal
2B = Bx16⁰ + 2x16¹
2B = 11x16⁰ + 2x16¹
2B = 11 + 32
2B ₍₁₆₎ = 43 ₍₁₀₎

decimal to binary
43 / 2 = 21, remains 1
21 / 2 = 10, remains 1
10 / 2 = 5, remains 0
5 / 2 = 2, remains 1
2 / 2 = 1, remains 0
1 / 2 = 0, remains 1
43 ₍₁₀₎ = 101011 ₍₂₎

2B hexadecimal number equal to 101011 binary number
2B ₍₁₆₎ = 101011 ₍₂₎

2. DAD ₍₁₆₎ = ? ₍₂₎
hexadecimal to decimal
DAD = Dx16⁰ + Ax16¹ + Ax16²
DAD = 13x16⁰ + 10x16¹ + 13x16²
DAD = 13 + 160 + 3328
DAD ₍₁₆₎ = 3501 ₍₁₀₎

decimal to binary
3501 / 2 = 1750, remains 1
1750 / 2 = 875, remains 0
875 / 2 = 437, remains 1
437 / 2 = 218, remains 1
218 / 2 = 109, remains 0
109 / 2 = 54, remains 1
54 / 2 = 27, remains 0
27 / 2 = 13, remains 1
13 / 2 = 6, remains 1
6 / 2 = 3, remains 0
3 / 2 = 1, remains 1
1 / 2 = 0, remains 1
3501 ₍₁₀₎ = 110110101101 ₍₂₎

DAD hexadecimal number equal to 110110101101 binary number
DAD ₍₁₆₎ = 110110101101 ₍₂₎

3. FE01 ₍₁₆₎ = ? ₍₂₎
hexadecimal to decimal
FE01 = 1x16⁰ + 0x16¹ + Ex16² + Fx16³
FE01 = 1x16⁰ + 0x16¹ + 14x16² + 15x16³
FE01 = 1 + 0 + 3584 + 61440
FE01 ₍₁₆₎ = 65025 ₍₁₀₎

decimal to binary
65025 / 2 = 32512, remains 1
32512 / 2 = 16256, remains 0
16256 / 2 = 8128, remains 0
8128 / 2 = 4064, remains 0
4064 / 2 = 2032, remains 0
2032 / 2 = 1016, remains 0
1016 / 2 = 508, remains 0
508 / 2 = 254, remains 0
254 / 2 = 127, remains 0
127 / 2 = 63, remains 1
63 / 2 = 31, remains 1
31 / 2 = 15, remains 1
15 / 2 = 7, remains 1
7 / 2 = 3, remains 1
3 / 2 = 1, remains 1
1 / 2 = 0, remains 1
605025 ₍₁₀₎ = 1111111000000001 ₍₂₎

FE01 hexadecimal number equal to 1111111000000001 binary number
FE01 ₍₁₆₎ = 1111111000000001 ₍₂₎

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Octal numbers to hexadecimal numbers

Convert octal numbers to hexadecimal numbers
1. 73
2. 305
3. 5431

Completion:
1. 73 ₍₈₎ = ? ₍₁₆₎
* First, convert octal numbers to decimal numbers. Then, convert decimal numbers to hexadecimal numbers.

octal to decimal
73 = 3x8⁰ + 7x8¹
73 = 3 + 56
73 ₍₈₎ = 59 ₍₁₀₎

decimal to hexadecimal
59 / 16 = 3, remains 11 or B
3 / 16 = 0, remains 3
59 ₍₁₀₎ = 3B ₍₁₆₎

73 octal number equal to 3B hexadecimal number
73 ₍₈₎ = 3B ₍₁₆₎

2. 305 ₍₈₎ = ? ₍₁₆₎
octal to decimal
305 = 5x8⁰ + 0x8¹ + 3x8²
305 = 5 + 0 + 192
305 ₍₈₎ = 197 ₍₁₀₎

decimal to hexadecimal
197 / 16 = 12, remains 5
12 / 16 = 0, remains 12 or C
197 ₍₁₀₎ = C5 ₍₁₆₎

305 octal number equal to C5 hexadecimal number
305 ₍₈₎ = C5 ₍₁₆₎

3. 5431 ₍₈₎ = ? ₍₁₆₎
octal to decimal
5431 = 1x8⁰ + 3x8¹ + 4x8² + 5x8³
5431 = 1 + 24 + 256 + 2560
5431 ₍₈₎ = 2841 ₍₁₀₎

decimal to hexadecimal
2841 / 16 = 177, remains 9
177 / 16 = 11, remains 1
11 / 16 = 0, remains 11 or B
2841 ₍₁₀₎ = B19 ₍₁₆₎

5431 octal number equal to B19 hexadecimal number
5431 ₍₈₎ = B19 ₍₁₆₎

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Octal numbers to binary numbers

Convert octal numbers to binary numbers
1. 45
2. 700
3. 2021

Completion:
1. 45 ₍₈₎ = ? ₍₂₎
* First, convert octal numbers to decimal numbers. Then, convert decimal numbers to binary numbers.

octal to decimal
45 = 5x8⁰ + 4x8¹
45 = 5 + 32
45 ₍₈₎ = 37 ₍₁₀₎

decimal to binary
37 / 2 = 18, remains 1
18 / 2 = 9, remains 0
9 / 2 = 4, remains 1
4 / 2 = 2, remains 0
2 / 2 = 1, remains 0
1 / 2 = 0, remains 1
37 ₍₁₀₎ = 100101 ₍₂₎

45 octal number equal to 100101 binary number
45 ₍₈₎ = 100101 ₍₂₎

2. 700 ₍₈₎ = ? ₍₂₎
octal to decimal
700 = 0x8⁰ + 0x8¹ + 7x8²
700 = 0 + 0 + 448
700 ₍₈₎ = 448 ₍₁₀₎

decimal to binary
448 / 2 = 224, remains 0
224 / 2 = 112, remains 0
112 / 2 = 56, remains 0
56 / 2 = 28, remains 0
28 / 2 = 14, remains 0
14 / 2 = 7, remains 0
7 / 2 = 3, remains 1
3 / 2 = 1, remains 1
1 / 2 = 0, remains 1
448 ₍₁₀₎ = 111000000 ₍₂₎

700 octal number equal to 111000000 binary number
700 ₍₈₎ = 111000000 ₍₂₎

3. 2021 ₍₈₎ = ? ₍₂₎
octal to decimal
2021 = 1x8⁰ + 2x8¹ + 0x8² + 2x8³
2021 = 1 + 16 + 0 + 1024
2021 ₍₈₎ = 1041 ₍₁₀₎

decimal to binary
1041 / 2 = 520, remains 1
520 / 2 = 260, remains 0
260 / 2 = 130, remains 0
130 / 2 = 65, remains 0
65 / 2 = 32, remains 1
32 / 2 = 16, remains 0
16 / 2 = 8, remains 0
8 / 2 = 4, remains 0
4 / 2 = 2, remains 0
2 / 2 = 1, remains 0
1 / 2 = 0, remains 1
1041 ₍₁₀₎ = 10000010001 ₍₂₎

2021 octal number equal to 10000010001 binary number
2021 ₍₈₎ = 10000010001 ₍₂₎

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Binary numbers to hexadecimal numbers

Convert binary numbers to hexadecimal numbers
1. 11111
2. 1101110
3. 1110101010

Completion:
1. 11111 ₍₂₎ = ? ₍₁₆₎
* First, convert binary numbers to decimal numbers. Then, convert decimal numbers to hexadecimal numbers.

binary to decimal
11111 = 1x2⁰ + 1x2¹ + 1x2² + 1x2³ + 1x2⁴
11111 = 1 + 2 + 4 + 8 + 16
11111 ₍₂₎ = 31 ₍₁₀₎

decimal to hexadecimal
31 / 16 = 1, remains 15 or F
1 / 16 = 0, remains 1
31 ₍₁₀₎ = 1F ₍₁₆₎

11111 binary number equal to 1F hexadecimal number
11111 ₍₂₎ = 1F ₍₁₆₎

2. 1101110 ₍₂₎ = ? ₍₁₆₎
binary to decimal
1101110 = 0x2⁰ + 1x2¹ + 1x2² + 1x2³ + 0x2⁴ + 1x2⁵ + 1x2⁶
1101110 = 0 + 2 + 4 + 8 + 0 + 32 + 64
1101110 ₍₂₎ = 110 ₍₁₀₎

decimal to hexadecimal
110 / 16 = 6, remains 14 or E
6 / 16 = 0, remains 6
79 ₍₁₀₎ = 6E ₍₁₆₎

1101110 binary number equal to 6E hexadecimal number
1101110 ₍₂₎ = 6E ₍₁₆₎

3. 1110101010 ₍₂₎ = ? ₍₁₆₎
binary to decimal
1110101010 = 0x2⁰ + 1x2¹ + 0x2² + 1x2³ + 0x2⁴ + 1x2⁵ + 0x2⁶ + 1x2⁷ + 1x2⁸ + 1x2⁹
1110101010 = 0 + 2 + 0 + 8 + 0 + 32 + 0 + 128 + 256 + 512
1110101010 ₍₂₎ = 938 ₍₁₀₎

decimal to hexadecimal
938 / 16 = 58, remains 10 or A
58 / 16 = 3, remains 10 or A
3 / 16 = 0, remains 3
938 ₍₁₀₎ = 3AA ₍₁₆₎

1110101010 binary number equal to 3AA hexadecimal number
1110101010 ₍₂₎ = 3AA ₍₁₆₎

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Binary numbers to octal numbers

Convert binary numbers to octal numbers
1. 11101
2. 1001111
3. 1010101010

Completion:
1. 11101 ₍₂₎ = ? ₍₈₎
* First, convert binary numbers to decimal numbers. Then, convert decimal numbers to octal numbers.

binary to decimal
11101 = 1x2⁰ + 0x2¹ + 1x2² + 1x2³ + 1x2⁴
11101 = 1 + 0 + 4 + 8 + 16
11101 ₍₂₎ = 29 ₍₁₀₎

decimal to octal
29 / 8 = 3, remains 5
3 / 8 = 0, remains 3
29 ₍₁₀₎ = 35 ₍₈₎

11101 binary number equal to 35 octal number
11101 ₍₂₎ = 35 ₍₈₎

2. 1001111 ₍₂₎ = ? ₍₈₎
binary to decimal
1001111 = 1x2⁰ + 1x2¹ + 1x2² + 1x2³ + 0x2⁴ + 0x2⁵ + 1x2⁶
1001111 = 1 + 2 + 4 + 8 + 0 + 0 + 64
1001111 ₍₂₎ = 79 ₍₁₀₎

decimal to octal
79 / 8 = 9, remains 7
9 / 8 = 1, remains 1
1 / 8 = 0, remains 1
79 ₍₁₀₎ = 117 ₍₈₎

1001111 binary number equal to 117 octal number
1001111 ₍₂₎ = 117 ₍₈₎

3. 1010101010 ₍₂₎ = ? ₍₈₎
binary to decimal
1010101010 = 0x2⁰ + 1x2¹ + 0x2² + 1x2³ + 0x2⁴ + 1x2⁵ + 0x2⁶ + 1x2⁷ + 0x2⁸ + 1x2⁹
1010101010 = 0 + 2 + 0 + 8 + 0 + 32 + 0 + 128 + 0 + 512
1010101010 ₍₂₎ = 682 ₍₁₀₎

decimal to octal
682 / 8 = 85, remains 2
85 / 8 = 10, remains 5
10 / 8 = 1, remains 2
1 / 8 = 0, remains 1
682 ₍₁₀₎ = 1252 ₍₈₎

1010101010 binary number equal to 1252 octal number
1010101010 ₍₂₎ = 1252 ₍₈₎

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Decimal numbers to hexadecimal numbers

Convert decimal numbers to hexadecimal numbers
1. 128
2. 2015
3. 300000

Completion:
1. 128 ₍₁₀₎ = ? ₍₁₆₎
→ 128 / 16 = 8, remains 0
→ 8 / 16 = 0, remains 8
* Finish when meet zero (0) and then write remains numbers, from bottom to top.
128 decimal number equal to 80 hexadecimal number
128 ₍₁₀₎ = 80 ₍₁₆₎

2. 2015 ₍₁₀₎ = ? ₍₁₆₎
2015 / 16 = 125, remains 15 or F
125 / 16 = 7, remains 13 or D
7 / 16 = 0, remains 7
2015 decimal number equal to 7DF hexadecimal number
2015 ₍₁₀₎ = 7DF ₍₁₆₎

3. 300000 ₍₁₀₎ = ? ₍₁₆₎
300000 / 16 = 18750, remains 0
18750 / 16 = 1171, remains 14 or E
1171 / 16 = 73, remains 3
73 / 16 = 4, remains 9
4 / 16 = 0, remains 4
300000 decimal number equal to 493E0 hexadecimal number
300000 ₍₁₀₎ = 493E0 ₍₁₆₎

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Decimal numbers to octal numbers

Convert decimal numbers to octal numbers
1. 60
2. 133
3. 512

Completion:
1. 60 ₍₁₀₎ = ? ₍₈₎
→ 60 / 8 = 7, remains 4
→ 7 / 8 = 0, remains 7
* Finish when meet zero (0) and then write remains numbers, from bottom to top
60 decimal number equal to 74 octal number
60 ₍₁₀₎ = 74 ₍₈₎

2. 133 ₍₁₀₎ = ? ₍₈₎
133 / 8 = 16, remains 5
16 / 8 = 2, remains 0
2 / 8 = 0, remains 2
133 decimal number equal to 205 octal number
133 ₍₁₀₎ = 205 ₍₈₎

3. 512 ₍₁₀₎ = ? ₍₈₎
512 / 8 = 64, remains 0
64 / 8 = 8, remains 0
8 / 8 = 1, remains 0
1 / 8 = 0, remains 1
512 decimal number equal to 1000 octal number
512 ₍₁₀₎ = 1000 ₍₈₎

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Decimal numbers to binary numbers

Convert decimal numbers to binary numbers
1. 10
2. 31
3. 42

Completion:
1. 10 ₍₁₀₎ = ? ₍₂₎
→ 10 / 2 = 5, remains 0
→ 5 / 2 = 2, remains 1
→ 2 / 2 = 1, remains 0
→ 1 / 2 = 0, remains 1
* Finish when meet zero (0) and then write remains numbers, from bottom to top
10 decimal number equal to 1010 binary number
10 ₍₁₀₎ = 1010 ₍₂₎

2. 31 ₍₁₀₎ = ? ₍₂₎
31 / 2 = 15, remains 1
15 / 2 = 7, remains 1
7 / 2 = 3, remains 1
3 / 2 = 1, remains 1
1 / 2 = 0, remains 1
31 decimal number equal to 11111 binary number
31 ₍₁₀₎ = 11111 ₍₂₎

3. 42 ₍₁₀₎ = ? ₍₂₎
42 / 2 = 21, remains 0
21 / 2 = 10, remains 1
10 / 2 = 5, remains 0
5 / 2 = 2, remains 1
2 / 2 = 1, remains 0
1 / 2 = 0, remains 1
42 decimal number equal to 101010 binary number
42 ₍₁₀₎ = 101010 ₍₂₎

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Hexa decimal number

Hexa decimal number is system number who have 16 digit numbers, which is 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E and F, where:
A present of 10
B present of 11
C present of 12
D present of 13
E present of 14
F present of 15.
Hexa decimal number base 16 numeral system.

Hexa decimal number weights
16⁰ = 1 → first digit, weights one
16¹ = 16 → second digit, weights sixteen
16² = 256 → third digit, weights two hundred and six
16³ = 4096 → fourth digit, weights 512
16⁴ = 65536 → fifth digit, weights 4096
etc.

Example 1:
Convert Hexa decimal number 750 to decimal number

Completion:
750 ₍₁₆₎ = ? ₍₁₀₎
0 → 0 × 16⁰ = 0
5 → 5 × 16¹ = 80
7 → 7 × 16² = 7 × 256 = 1792
750 → 0 + 80 + 1792 = 1872
750 ₍₁₆₎ = 1872 ₍₁₀₎.

Example 2:
Convert Hexa decimal number 20BCA to decimal number

Completion:
20BCA ₍₁₆₎ = ? ₍₁₀₎
A → 10 × 16⁰ = 10
C → 12 × 16¹ = 192
B → 11 × 16² = 11 × 256 = 2816
0 → 0 × 16³ = 0
2 → 2 × 16⁴ = 2 × 65536 = 131072
20BCA → 10 + 192 + 2816 + 0 + 131072 = 134090
20BCA ₍₁₆₎ = 134090 ₍₁₀₎.

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Octal number

Octal number is system number who have 8 digit numbers, which is 0, 1, 2, 3, 4, 5, 6 and 7. Octal number base 8 numeral system.

Octal number weights
8⁰ = 1 → first digit, weights one
8¹ = 8 → second digit, weights eight
8² = 64 → third digit, weights sixty four
8³ = 512 → fourth digit, weights 512
8⁴ = 4096 → fifth digit, weights 4096
etc.

Example 1:
Convert Octal number 370 to decimal number

Completion:
370 ₍₈₎ = ? ₍₁₀₎
0 → 0 × 8⁰ = 0
7 → 7 × 8¹ = 56
3 → 3 × 8² = 192
370 → 0 + 56 + 192 = 248
370 ₍₈₎ = 248 ₍₁₀₎

Example 2:
Convert Octal number 55017 to decimal number

Completion:
55017 ₍₈₎ = ? ₍₁₀₎
7 → 7 × 8⁰ = 7
1 → 1 × 8¹ = 8
0 → 0 × 8² = 0
5 → 5 × 8³ = 2560
5 → 5 × 8⁴ = 20480
55017 → 7 + 8 + 0 + 2560 + 20480 = 23055
55017 ₍₈₎ = 23055 ₍₁₀₎

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Decimal number

Decimal number is system number who have 10 digit numbers, consist of 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. Decimal number base 10 numeral system, and it's the most used in the system numbers.

Decimal number weights
10⁰ = 1 → first digit, weights one
10¹ = 10 → second digit, weights ten
10² = 100 → third digit, weights hundred
10³ = 1000 → fourth digit, weights thousand
10⁴ = 1000 → fifth digit, weights ten thousand
etc.

Example 1:
Describe a decimal number 2015 in the system numbers

Completion:
2015 ₍₁₀₎ =
5 → 5 × 10⁰ = 5
1 → 1 × 10¹ = 10
0 → 0 × 10² = 0
2 → 2 × 10³ = 2000
2015 → 5 + 10 + 0 + 2000 = 2015

Example 2:
Describe a decimal number 1000518 in the system numbers

Completion:
1000518 ₍₁₀₎ =
8 → 8 × 10⁰ = 8
1 → 1 × 10¹ = 10
5 → 5 × 10² = 500
0 → 0 × 10³ = 0
0 → 0 × 10⁴ = 0
0 → 0 × 10⁵ = 0
1 → 1 × 10⁶ = 1000000
1000518 → 8 + 10 + 500 + 0 + 0 + 0 + 1000000 = 1000518.

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