Convert decimal to binary

1. DECIMAL BINARY

2. The Decimal System (Base) 10
• The word decimal is derived from the Latin root
decem(ten)
• Base b = 10
• Ten symbols: S = {0,1,2,3,4,5,6,7,8,9}
Example:45,452,501,4521
• The symbols in this system are often referred to
as decimal digits or just digits.

3. BINARY
• The word binary is derived from the Latin root
• bini (double).
• Base b = 2.
• Ten symbols: S = {0, 1}
Binary is a base 2 number system invented by Gottfried Leibniz that is made up of only two
numbers: 0 and 1. This number system is the basis for all binary code, which is used to write
data such as the instructions that computer processors use, or the digital text you read every
day.

4. DECIMAL
BINARY

5. DECIMAL BINARYTO
10
=
212 / 2 RESULT 106 REMAINDER 0
106 /
53
26
13
6
3
1
2 RESULT 53 REMAINDER 0
/
/
/
/
/
/
2 RESULT 26 REMAINDER
02 RESULT 13 REMAINDER
2 RESULT 6 REMAINDER
1
1
2 RESULT 3 REMAINDER 0
2 RESULT 1 REMAINDER 1
2 RESULT 0 REMAINDER 1
1 1 0 1 0 1 0 0
2

6. DECIMAL BINARYTO
10
=
5862 / 2 RESULT 2931 REMAINDER 0
1 0 1 1 0 1 1 1
2
2931 / 2 RESULT 1465 REMAINDER 1
1465 / 2 RESULT 732 REMAINDER 1
732 / 2 RESULT 366 REMAINDER 0
366 / 2 RESULT 183 REMAINDER 0
183 / 2 RESULT 91 REMAINDER 1
91 / 2 RESULT 45 REMAINDER 1
45 / 2 RESULT 22 REMAINDER 1
22 / 2 RESULT 11 REMAINDER 0
11 / 2 RESULT 5 REMAINDER 1
5 / 2 RESULT 2 REMAINDER 1
2 / 2 RESULT 1 REMAINDER 0
1 / 2 RESULT 0 REMAINDER 1
0 0 1 1 0

7. DECIMAL BINARYTO
3014 10
6489 10
1256 10
2245 10
=
=
=
=752 10
=
101111000110 2
1100101011001
10011101000
100011000101
1011110000
2
2
2
2
1.
2.
3.
4.
5.

8. BINARY
DECIMAL

9. 128 64 32 16 8 4 2 1

10. DECIMALBINARY TO
2
2
0
2
1
2
2
2
3
2
4
1 X 10 X 21 X 40 X 81 X 16
01234
16 0 4 0 1+ + + + = 21
21
10
=
128 64 32 16 8 4 2 1
THE BINARY TABLE

11. DECIMALBINARY TO
2
2
0
2
1
2
2
2
3
2
4
1 X 11 X 20 X 40 X 81 X 16
01234
339
10
=
128 64 32 16 8 4 2 1
THE BINARY TABLE
2
5
2
6
2
7
2
8
0 X 32
5
1 X 64
6
0 X 128
7
1 X 256
8
+ + + + + + + +256 0 64 0 16 0 0 2 1 = 339

12. DECIMALBINARY TO
2 10
=
1248163264128256
256 64+ + 2+ =32 + 8
362
362

13. DECIMALBINARY TO
10
=
=
=
=
=
1001000101001 2
1.
2.
3.
4.
5.
10111000111100
10011110011101
11000010101001
10101110100101
2
2
2
2
4649
11836
10141
12457
11173
10
10
10
10

15. 10=
=
=
=
=
1111011101010 2
1.
2.
3.
4.
5.
100101011010
11001010111
11010111010100
111000010101000
0
2
2
2
2
7914
2394
1623
13780
57680
10
10
10
10
6.
7.
8.
9.
10.
= 1011000010011111
2
45215
10
= 110001101000110
2
25414
10
= 1010010111010011
2
42451
10
= 10010011010010100
2
75412
10
= 11010000100111110000
2
854512
10