text: how do you count in binary? 11111101 i dont know what it means and its ticking me off. 101 11101 111100 what numbers do they represent any way? all i know about them is that 1 stands for 'on' and 0 stands for 'off' but i heard that you can use them to count. any guesses? hi:  the truth table for binary addition is :  0+0 =0  0+1 =1 1+0 =1 1+1 = 10 { the one is carried over to the next digit}  for example 7 + 3 = 10 decimal   111 is 7 decimal in binary  because 4(1)+2(1) +1(1) = 4+2+1=7 011 is 3 decimal in binay   because 4(0) +2(1) +1(1) = 2+1= 3   okay let add   { ignore the # symbol it for postioning thing here it add nothing to the problem okay.  ## 111 #+ 011 ----------   from our truth table of adding number 1+1 = 10  so :  ####1 - ( carry section here) ## 111 #+ 011 ---------- #####0  and 1+1= 10 however we have a carry of 1here so get added on  so 1+1+1= 11 so we do the following:  ## 11 - ( carry section here) ## 111 #+ 011 ---------- ### 10  now we add the next column. like so: 1+0= 1 but we have a carry of 1 so: 1+1= 10 and we do like so :  # 111 -( carry section here)  ## 111 #+ 011 ---------- ##010   now in the next column we have a 1 in the carry section but nothing in that column so a zero is put here and added. so 1+0 = 1. and we do the following:   #111 -( carry section here) +0111 ##011 ---------- #1010   and 1010 is the answer because   8(1)+(0)4+(1)2+(0)1= 8+2 = 10 decimal   so 3 decimal which is 011 binary and 7 decimal in binary is 111 when add together is 10 decimal; which in binary is 1010   and that is how you add numbers in binary  mulitiply in is the same as multiplication of 1 and 0   for example let do 5 times 5 in binary    so 5= 101 binary    ##101 #x101 ---------- starting with the right column multiply 101 by 1 which equals 101  so :   ##101 #x101 ---------- ### 101  now with the next colum from the right multiply the 101 by 0 it equals 0   so    ##101 #x101 ---------- ### 101 ## 000  now for the final column multiply 101 by 1 and it equal 101   so    ##101 #x101 ---------- ### 101 ## 000 # 101 -------------   add the partial additions here to get :  ##101 #x101 ---------- ### 101 ## 000 # 101 ------------- 11001   let see if this is the right answer   16(1) +8(1) +4(0) +2(0)+1(1) = 16 + 8+1= 25  so 5 x 5 = 25  or 101(5 binary) time 101( 5 binary) = 11001(25 binary )  this check out    division is a bit more involved but lets do it:  5 divided by 2   so 5 =101 and 2= 10   setup the problem like so:   ##___________________ 10/101.00000000000000   so let start by how many 10 will go into 10 the answer 1   so   ##_1_________________ 10/101.00000000000000 -10 -----------  ### 1  how many 10 will go in to 1 answer 0 so   ##_10._________________ 10/101.00000000000000 -10 -----------  ####1 ### -0  ------------ ####10   put our decimal point here{ because we reached it } and  how many 10 will go into 10 answer 1   so :  ##_10.1_________________ 10/101.00000000000000 -10 -----------  ####1 ### -0  ------------ ####10  ### -10 ---------------  ######0   no need to go any farther all the rest are zeros from here  so the answer is 10.1 binary which is   2(1)+ 1(0) + (1)(1/2) = 2 1/2 decimal which is the correct answer   use this  to help you :      4096, 2048, 1024, 512 ,  256 , 128 ,  64 , 32 , 16 , 8, 4, 2  1 ##0####0####0###0####0####1###1###1###1# 1#1#0#1   put in the 1's and zero's in the 2 place holder like i got above here.  multiply the 1 and the zeros where they appear in the 2's place holder { i ignore the the leading zeros here} like so:   128(1)+64(1)+32(1)+ 16(1)+8(1) +4(1) +2(0)+1(1)   128+64+32+16+8+4+1 =  253    so: 11111101 binary is 253 decimal   the best way to do this is to set your computer's calulator to binary by clicking the bin circle enter your binary number and select the dec circle to tell you what the decimal number is                                                                                                                                                                                              hope this helps