# Binary

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The following tutorial will help you understand the conversion from binary to decimal numbers and decimal to binary numbers, quickly and easily…. Decimal to Binary
Decimal numbers use Base 10
Binary numbers use Base 2
8 bits = 1 Byte
Study the following chart and the comments by each line or section… | | 8 bits | 7 bits | 6 bits | 5 bits | 4 bits | 3 bits | 2 bits | 1bit | Base 2 | | 27 | 26 | 25 | 24 | 23 | 22 | 21 | 20 | DecimalWeight value of each bit | | 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 | Decimal to binary… | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | | 3 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | | 4 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | | 5 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | | 6 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 |
Do you see the pattern?
1 = 00000001
0+0+0+0+0+0+1 (the 1 bit is in the 20 position, the 20 position value="1).
2 = 00000010
0+0+0+0+0+0+1+0 = (the 1 is in the 21 position, the 21 position value="2)
3 = 00000011
0+0+0=0+0+0+1+1 = (the 1 is in the 21 and 20 positions, the 20 value="1" and the 21 value="2" therefore, 2 +1 = 3).
4 = 00000100
0+0+0+0+0+1+0+0 = (the 1 is in the 22 position. The 22 value="4)
Always start from left to right on the chart (highest to lowest number).
Try the following exercises…
Change the following decimal numbers into binary and vice-versa. I have done the first one for you, you do the rest... Make sure you know where your digits are coming from… Decimal | Binary | “Reasoning” | Ex. 234 | 11101010 | 128 +64 +32+0+8+0+2+0 = 234 | 125 | | | 86 | | | 244 | | | 250 | | | 8 | | | 23 | | | 152 | | | 19 | | | Binary | Decimal | “Reasoning” | Ex. 11110000 | 240 | 128+64+32+16+0+0+0+0=240 | 11100000 | | | 10101010 | | | 11001100 | | | 00000110 | | | 10001001 | | |...

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