Binary Addition

Consider the addition of decimal numbers:
23 +48 _
We begin by adding 3+8=11. Since 11 is greater than 10, a one is put into the 10's column (carried), and a 1 is recorded in the one's column of the sum. Next, add {(2+4) +1} (the one is from the carry)=7, which is put in the 10's column of the sum. Thus, the answer is 71. Binary addition works on the same principle, but the numerals are different. Begin with one-bit binary addition:
0 0 1 +0 +1 +0 _ _ _ 0 1 1
1+1 carries us into the next column. In decimal form, 1+1=2. In binary, any digit higher than 1 puts us a column to the left (as would 10 in decimal notation). The decimal number "2" is written in binary notation as "10" (1*2^1)+(0*2^0). Record the 0 in the ones column, and carry the 1 to the twos column to get an answer of "10." In our vertical notation,
1 +1 _ 10
The process is the same for multiple-bit binary numbers:
1010 +1111 ____
Step one: Column 2^0: 0+1=1. Record the 1. Temporary Result: 1;
Carry: 0
Step two:
Column 2^1: 1+1=10. Record the 0, carry the 1. Temporary Result: 01; Carry: 1 Step three: Column 2^2: 1+0=1 Add 1 from carry: 1+1=10. Record the 0, carry the 1. Temporary Result: 001; Carry: 1 Step four: Column 2^3: 1+1=10. Add 1 from carry: 10+1=11. Record the 11. Final result: 11001 Alternately:
11 (carry) 1010 +1111 ____ 11001
Always remember 0+0=0 1+0=1 1+1=10
Try a few examples of binary addition:
111 101 111 +110 +111 +111 ____ ___ ___