Number Systems
1. Decimal Numbers
Decimal Numbers
Decimal numbers are numbers with a base 10,
disimbulkandengan 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
N = an x 10 n + an-1 x 10 n-1 + .... + A1 x + a0 x 10 1
10 0 + a-1 x 10 -1 + a-2 x 10 -2 + .... + A-n x 10-n
N = 1 0 2 5 7 Decimal Numbers
4 3 2 1 0 Number of Digits
N = 1 x 10 4 + 0 x 10 3 + 2x + 5x 10 2 10 1 + 7 x 10 0
N = 10000 + 0 + 200 + 50 + 7
N = 10 257
2. Binary Numbers
Binary Numbers
Binary numbers are base 2 bilangandengan,
disimbulkandengan 0, 1
To make the binary number to decimal
Following manner:
N = an x 2 n + an-1 x 2 n-1 + .... + A1 + a0 x 2 1 x 2 0 + a-1 x 2 -
1 + a-2 x 2 2 + .... + A-n x 2-n
N = 1 0 1 1 0 Binary Numbers
4 3 2 1 0 Number of Digits
N = 1 x 2 4 + 0 x 2 3 + 1 x 2 2 + 1 x 2 1 + 0 x 2 0
N = 1 x 16 + 0 x 8 + 1 x 4 + 1 x 2 + 0 X 1
N = 16 + 4 + 2
N = 22 ß Decimal numbers
Decimal Numbers into Binary Numbers
Binary Numbers Decimal numbers can be searched from the
continuously divide by 2, the last remnant of
until the first binary merupakanangka
be obtained
N = 22 ß Decimal Numbers
22: 2 = 11 remainder 0
11: 2 = 5 remainder 1
5: 2 = 2 remainder 1
2: 2 = 1 remainder 0
1: 2 = 0 remainder 1
N = 22 (10) = 10110 (2)
3. Octal Numbers
Octal Numbers
Octal numbers are numbers with base 8,
disimbulkandengan 0, 1, 2, 3, 4, 5, 6, 7
To make an octal number to decimal
dengancara as follows:
N = an x 8 n + an-1 x 8 n-1 + .... + A1 + a0 x 8 1 x 8 0 + a-1 x 8 -
1 + a-2 x 8 2 + .... + A-n x 8-n
N = 1 0 2 7 1 Octal Numbers
4 3 2 1 0 Number of Digits
N = 1 x 8 4 + 0 x 83 + 2 x 8 2 + 7x + 1x 8 1 8 0
N = 1 x 4096 + 0 x 512 + 2 x 64 + 7 x 8 + 1 X 1
N = 4096 + 128 + 56 + 1
N = 4281 ß Decimal numbers
Decimal Numbers to Octal Numbers
Octal numbers can be searched from Decimal numbers with
continuously dividing by 8, the last remnant of
until the first binary merupakanangka
be obtained
N = 4281 Decimal Numbers
4281: 8 = 1 x 4096 the remaining 185
185: 8 = 0 x 512 residual 185
185: 8 = 2 x 64 remainder 57
57: 8 = 7 x 8 remaining 1
1: 8 = 1 x 1 remainder 0
N = 4281 (10) = 10271 (8)
Binary to Octal Numbers Numbers
Octal numbers can be searched from the binary number with
To group 3, 3, 3 from the right
N = 1 | 1 0 1 | 1 1 0 | 1 1 0 Binary Numbers
1 5 6 6 Octal Numbers
N = 1101110110 (2) = 1566 (8)
4. Hexadecimal Numbers
Hexadecimal Numbers
Hexadecimal numbers are numbers with a base 16, disimbulkan
with 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, b, C, D, E, F
To make hexadecimal numbers into numbers
decimal in the following ways:
N = an x 16 n + an-1 x 16 n-1 + .... + A1 + a0 x 16 1 x 16 0 + a-1
x 16 -1 + a-2 x 16 -2 + .... + A-n x 16-n
N = 1 0 A 5 B ß Hexadecimal Numbers
4 3 2 1 0 ß Number of Digits
N = 1 x 16 4 + 0 x 163 + Ax 16 2 + 5 x 16 1 + B x 16 0
N = 1 x 65 536 + 0 x 4096 + A x 256 + 5 x 16 + BX 1
N = 65536 + 2560 + 80 + 11
N = 68 187 ß Decimal numbers
Binary Numbers to Hexadecimal Numbers
Hexadecimal numbers can be searched from the binary number
denganmengelompokan 4, 4, 4 from the right
N = 1 1 0 1 1 1 0 1 1 0 Binary Numbers
11 0 1 1 1 0 1 1 0
3 7 6 ß Hexadecimal Numbers
N = 1101110110 (2) = 376 (16)
15 1111 17 F
14 1110 16 E
13 1101 15 D
12 1100 14 C
11 1011 13 B
10 1010 12 A
09 1001 11 9
08 1000 10 8
07 0111 07 7
06 0110 06 6
05 0101 05 5
04 0100 04 4
03 0011 03 3
02 0010 02 2
01 0001 01 1
00 0000 00 0
1. Decimal Numbers
Decimal Numbers
Decimal numbers are numbers with a base 10,
disimbulkandengan 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
N = an x 10 n + an-1 x 10 n-1 + .... + A1 x + a0 x 10 1
10 0 + a-1 x 10 -1 + a-2 x 10 -2 + .... + A-n x 10-n
N = 1 0 2 5 7 Decimal Numbers
4 3 2 1 0 Number of Digits
N = 1 x 10 4 + 0 x 10 3 + 2x + 5x 10 2 10 1 + 7 x 10 0
N = 10000 + 0 + 200 + 50 + 7
N = 10 257
2. Binary Numbers
Binary Numbers
Binary numbers are base 2 bilangandengan,
disimbulkandengan 0, 1
To make the binary number to decimal
Following manner:
N = an x 2 n + an-1 x 2 n-1 + .... + A1 + a0 x 2 1 x 2 0 + a-1 x 2 -
1 + a-2 x 2 2 + .... + A-n x 2-n
N = 1 0 1 1 0 Binary Numbers
4 3 2 1 0 Number of Digits
N = 1 x 2 4 + 0 x 2 3 + 1 x 2 2 + 1 x 2 1 + 0 x 2 0
N = 1 x 16 + 0 x 8 + 1 x 4 + 1 x 2 + 0 X 1
N = 16 + 4 + 2
N = 22 ß Decimal numbers
Decimal Numbers into Binary Numbers
Binary Numbers Decimal numbers can be searched from the
continuously divide by 2, the last remnant of
until the first binary merupakanangka
be obtained
N = 22 ß Decimal Numbers
22: 2 = 11 remainder 0
11: 2 = 5 remainder 1
5: 2 = 2 remainder 1
2: 2 = 1 remainder 0
1: 2 = 0 remainder 1
N = 22 (10) = 10110 (2)
3. Octal Numbers
Octal Numbers
Octal numbers are numbers with base 8,
disimbulkandengan 0, 1, 2, 3, 4, 5, 6, 7
To make an octal number to decimal
dengancara as follows:
N = an x 8 n + an-1 x 8 n-1 + .... + A1 + a0 x 8 1 x 8 0 + a-1 x 8 -
1 + a-2 x 8 2 + .... + A-n x 8-n
N = 1 0 2 7 1 Octal Numbers
4 3 2 1 0 Number of Digits
N = 1 x 8 4 + 0 x 83 + 2 x 8 2 + 7x + 1x 8 1 8 0
N = 1 x 4096 + 0 x 512 + 2 x 64 + 7 x 8 + 1 X 1
N = 4096 + 128 + 56 + 1
N = 4281 ß Decimal numbers
Decimal Numbers to Octal Numbers
Octal numbers can be searched from Decimal numbers with
continuously dividing by 8, the last remnant of
until the first binary merupakanangka
be obtained
N = 4281 Decimal Numbers
4281: 8 = 1 x 4096 the remaining 185
185: 8 = 0 x 512 residual 185
185: 8 = 2 x 64 remainder 57
57: 8 = 7 x 8 remaining 1
1: 8 = 1 x 1 remainder 0
N = 4281 (10) = 10271 (8)
Binary to Octal Numbers Numbers
Octal numbers can be searched from the binary number with
To group 3, 3, 3 from the right
N = 1 | 1 0 1 | 1 1 0 | 1 1 0 Binary Numbers
1 5 6 6 Octal Numbers
N = 1101110110 (2) = 1566 (8)
4. Hexadecimal Numbers
Hexadecimal Numbers
Hexadecimal numbers are numbers with a base 16, disimbulkan
with 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, b, C, D, E, F
To make hexadecimal numbers into numbers
decimal in the following ways:
N = an x 16 n + an-1 x 16 n-1 + .... + A1 + a0 x 16 1 x 16 0 + a-1
x 16 -1 + a-2 x 16 -2 + .... + A-n x 16-n
N = 1 0 A 5 B ß Hexadecimal Numbers
4 3 2 1 0 ß Number of Digits
N = 1 x 16 4 + 0 x 163 + Ax 16 2 + 5 x 16 1 + B x 16 0
N = 1 x 65 536 + 0 x 4096 + A x 256 + 5 x 16 + BX 1
N = 65536 + 2560 + 80 + 11
N = 68 187 ß Decimal numbers
Binary Numbers to Hexadecimal Numbers
Hexadecimal numbers can be searched from the binary number
denganmengelompokan 4, 4, 4 from the right
N = 1 1 0 1 1 1 0 1 1 0 Binary Numbers
11 0 1 1 1 0 1 1 0
3 7 6 ß Hexadecimal Numbers
N = 1101110110 (2) = 376 (16)
15 1111 17 F
14 1110 16 E
13 1101 15 D
12 1100 14 C
11 1011 13 B
10 1010 12 A
09 1001 11 9
08 1000 10 8
07 0111 07 7
06 0110 06 6
05 0101 05 5
04 0100 04 4
03 0011 03 3
02 0010 02 2
01 0001 01 1
00 0000 00 0
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