Binary is a system that uses only two digits, 1 and 0, to represent all data in computers. It represents on and off signals that computers can understand. A binary number represents its value by powers of two, with the first digit having a value of 1, the second 21=2, the third 22=4, and so on. To convert a binary number to decimal, you add up the place values of the 1s in the binary number. Letters are also represented in binary by assigning numeric values to different parts of an 8-digit binary number.

1. An Introduction To Binary By Chris Price

2. What is Binary? Binary is a way to express letters and numbers that uses ones and zeros to represent on and off’s in a string of information in a computer. Binary Only consists of 2 variables and they are ones and zeros. Binary was thought of because it is an easier way to express numbers and letters to a computer.

3. Understanding Base Ten Base Ten is the common way of expressing numbers to humans and some animals. Base Ten consists of these characters: 1, 2, 3, 4, 5, 6, 7, 8, 9, and 0. 215 in Base Ten is two hundred + ten + five. But how do we arrive at this number?

4. Understanding Base Ten Here’s how: We know that 2 is in the hundreds spot thus giving it a numerical weight of x100, 1 is in the tens spot giving it a numerical weight of x10, and 5 is in the ones place giving it a numerical weight of x1. So 215 is really (2 x 100)+(1 x 10)+(5 x 1). 10 to the power of 0 is 1, 10 to the power of 1 is 10, 10 to the power of 2 is 100, and ect. Hundreds Tens Ones 2 5 1 10 10 10 x100 x1 x10 0 1 2

5. Base 2 or Binary But what about Base 2? The base 2 system only uses two numbers, which are: 1 and 0. 1 meaning on and zero meaning off. A Base 2 number or letter is a series of on and off. Here is an example: 0110 is off, on, on, off.

6. Base 2 Here’s the a Base 2 Chart: 1 1 1 0 0 Four’s Ones Two’s Eight’s Sixteen’s 2 2 2 2 2 2 1 0 3 4 x1 x16 x8 x4 x2

7. Base 2 This is what we were taught by default: since we see the first one in the second spot which we think is the tens place, we think the first one has a weight of 10. But that is not the case with Base 2. The first one doesn’t have a weight of 10 but a weight of 2. The second one doesn’t have a weight of 100 but a weight of 4. The weights of the number keeps doubling from right to left starting with 1 on the far left column. So 10110 is actually: (1x16)+(0x8)+(1x4)+(1x2)+(0x1)=22

8. Base 2 Numbers Here’s how to convert a binary number into a Base 10 number (decimal): (Only worry about the ones, the zero’s have a value of nothing.) Start by figuring out the value of the ones. For this instance the first one has a value of 2, the next has a value of 4 and the last has a value of 16. Like I said earlier, the values of the number columns double from right to left starting with the column farthest right being one. Then add up the values of the ones. 2+4+16=22 10110=22 The Zero’s don’t have any value so forget about them!!! 1 1 1 0 0 Four’s Ones Two’s Eight’s Sixteen’s 2 2 2 2 2 2 1 0 3 4 x1 x16 x8 x4 x2

9. Binary Letters Here’s how to convert binary letters to the alphabet: 01011010 01 tells the computer that it is a binary letter not a number. The next number decides whether it is a capital or a lowercase letter. 1=lowercase 0=capital The next number decides which letter group it is in. 1= p, q, r, s, t, u, v, w, x, y, z, 0= a, b, c, d, e, f, g, h, I, j, k, l, m, n, o, For the last four numbers, this is the layout. 1 0 1 0 8 4 2 1 But since there are zeros, we forget about them.

10. Binary Letters 1010 8 2 So we add them up. 8+2=10 We then go 10 letters down. p, q, r, s, t, u, v, w, x, y, z 01011010=Y

11. Conclusion Binary is a way to express numbers and letters using ones and zeros. The ones and zeros represent ons and offs. Binary is also the way computers understand letters and numbers. it is an easier way to express it to them. Binary numbers are also known as Base 2. I hope that this has helped you understand binary.