Number Systems

Like decimal each column of a binary number is a multiply of a power of base, but the base is two not ten. Again like decimal binary has as many digit types as its base, i.e., 0 and 1.

$2^{5}$	$2^{4}$	$2^{3}$	$2^{2}$	$2^{1}$	$2^{0}$
$32$	$16$	$8$	$4$	$2$	$1$

So, $101111$ in binary represents

2^{5} + 2^{3} + 2^{2} + 2^{1} + 2^{0} = 32 + 8 + 4 + 2 + 1 = 47

in decimal

i.e., $101111_{2} = 47_{10}$

Decimal	Binary	Sum of powers of two
0	00000	0+0+0+0+0
1	00001	0+0+0+0+1
2	00010	0+0+0+2+0
3	00011	0+0+0+2+1
4	00100	0+0+4+0+0
5	00101	0+0+4+0+1
6	00110	0+0+4+2+0
7	00111	0+0+4+2+1
8	01000	0+8+0+0+0
9	01001	0+8+0+0+1
10	01010	0+8+0+2+0
11	01011	0+8+0+2+1
12	01100	0+8+4+0+0
13	01101	0+8+4+0+1
14	01110	0+8+4+2+0
15	01111	0+8+4+2+1
16	10000	16+0+0+0+0
17	10001	16+0+0+0+1
18	10010	16+0+0+2+0
19	10011	16+0+0+2+1
20	10100	16+0+4+0+0
21	10101	16+0+4+0+1
22	10110	16+0+4+2+0
23	10111	16+0+4+2+1
24	11000	16+8+0+0+0
25	11001	16+8+0+0+1
26	11010	16+8+0+2+0
27	11011	16+8+0+2+1
28	11100	16+8+4+0+0
29	11101	16+8+4+0+1
30	11110	16+8+4+2+0
31	11111	16+8+4+2+1

Binary Numbers

Binary Basics

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Roman Numerals.

Roman Numerals are written with combinations of seven letters from the Latin alphabet, each letter with a fixed positive whole number value:

I	V	X	L	C	D	M
1	5	10	50	100	500	1000

By collecting combinations, largest value left-most and smallest right-most, numbers can be formed:

Decimal Number	Roman Numeral
1	I
2	II
3	III
4	IIII (IV)
5	V
6	VI
7	VII
8	VIII
9	VIIII (IX)
10	X
11	XI
12	XII
13	XIII
14	XIIII (XIV)
15	XV
16	XVI
17	XVII
18	XVIII
19	XVIIII (XIX)
20	XX
30	XXX
40	XXXX (XL)
50	L

Decimal Number	Roman Numeral
60	LX
70	LXX
80	LXXX
90	LXXXX (XC)
99	LXXXXVIIII (XCIX)
100	C
110	CX
200	CC
300	CCC
400	CCCC (CD)
500	D
600	DC
700	DCC
800	DCCC
900	DCCCC (CM)
999	DCCCCLXXXXVIIII (CMXCIX)
1000	M
1331	MCCCXXXI
1967	MDCCCCLXVII (MCMLXVII)
1999	MDCCCCLXXXXVIIII (MCMXCIX)
2006	MMVI
2024	MMXXIIII (MMXXIV)

Ref: en.wikipedia.org/wiki/Roman_numerals

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$0.012 = \frac{3}{250} = 1.2 % = 1.2 \times 10^{-2} = {0.00000011}_{2}$

(Decimals, Fractions, Percentages, Standard Form, Binary)

Common decimal, percentages and fractions compared

other systems

Roman Numerals

Cuneiform Numbers

Decimals

Recurring Decimal

Fractions

Remember

Percentages

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Standard Form

$A \times 10^{n}$

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Binary

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Binary Numbers

Binary Basics

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Roman Numerals.

Videos and Questions:

0.012 =3250 =1.2⁢% =1.2×10-2 = 0.000000112

(Decimals, Fractions, Percentages, Standard Form, Binary)

Common decimal, percentages and fractions compared

other systems

Roman Numerals

Cuneiform Numbers

Decimals

Recurring Decimal

Fractions

Remember

Percentages

See also Interest

Standard Form

A×10n

Videos and Questions:

Binary

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Binary Numbers

Binary Basics

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Roman Numerals.

Videos and Questions:

$0.012 = \frac{3}{250} = 1.2 % = 1.2 \times 10^{-2} = {0.00000011}_{2}$

$A \times 10^{n}$

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