tag:blogger.com,1999:blog-4632435085083780021.post4943859657750898498..comments2017-12-02T02:22:00.572-08:00Comments on Educational Radio Net: Bits, Nibbles, Bytes, and Words, Lee Bond N7KCBob Hellinghttp://www.blogger.com/profile/02352636352618704676noreply@blogger.comBlogger3125tag:blogger.com,1999:blog-4632435085083780021.post-10530086158381787912009-10-01T15:43:48.055-07:002009-10-01T15:43:48.055-07:00Strictly, you are limiting to non-negative integer...Strictly, you are limiting to non-negative integers, also known as unsigned integers. The set of positive integers does not include zero, and is also called the counting numbers, which begins at one. You need zero to have 256 distinct combinations for eight bits, 0 through 255, and 65536 combinations for 16 bits, 0 through 65535.Doug KD7KKRhttps://www.blogger.com/profile/10821475837050189513noreply@blogger.comtag:blogger.com,1999:blog-4632435085083780021.post-68804834017982314402009-10-01T15:38:17.682-07:002009-10-01T15:38:17.682-07:00Since you were talking about eight binary digits, ...Since you were talking about eight binary digits, you should not have included nine place values. 256 is the place value for the ninth digit.Doug KD7KKRhttps://www.blogger.com/profile/10821475837050189513noreply@blogger.comtag:blogger.com,1999:blog-4632435085083780021.post-41054192636994617762009-10-01T15:30:18.849-07:002009-10-01T15:30:18.849-07:00In the system of bins, for decimal, there should b...In the system of bins, for decimal, there should be 9 marbles in each column. The marbles are not symbols. The ten symbols 0 - 9 stand for zero through nine marbles in the upper bin. If you have 10 marbles, you have too many. Before the first count, you have no marbles in the upper bin, which corresponds to the symbol zero. When you begin the tenth count, you already have nine marbles in the upper bin, so you have no marbles in the lower bin. This is how you know to return all the marbles from the upper bin back to the lower bin and move one marble up in the next column, representing 10. You always have one less marble in each column than the base you are using. For binary, you have only one marble in each column, either in the lower bin (0) or the upper bin (1). When you use symbols instead of marbles in bins, you need ten symbols for decimal or two for binary because you need zero as a place holder. When you use bins, the column of bins is the place holder. I was going to suggest comparing the bin system with the system used on an abacus, but it turns out several different systems are used with an abacus, so some have 9 beads per column, some have 10; some have two groups of beads per column, with 4 and 1 beads (the extra bead denoting 5, as in: 0+0, 0+1, 0+2, 0+4, 5+0, 5+1, 5+2, 5+3, 5+4), some have 5 and 2 beads, and can be used for either decimal or hexadecimal.Doug KD7KKRhttps://www.blogger.com/profile/10821475837050189513noreply@blogger.com