Intro to Digital Logic

1. Intro to Digital Logic

2. Binary Number System • Binary is a number system much like decimal • Decimal is a base 10 number system • Almost every civilization uses a base 10 number system. Why? • What do we have 10 of? • Binary is a base 2 number system • Binary is only represented as 1 and 0 • Therefore, the first number in binary is… • 0! Same as decimal! The next number is • 1 Same again! The next would be? • 10? What the?

3. Binary Number System • Decimal’s next number would be 2, but seeing as we don’t have 2’s in binary, we must add a place • 10! • Next would be? • 11 • and after that? • 100!

4. How to tell what we are talking about • Is 100 and 100 the same number in binary and decimal? • NO! • How do we tell which we are talking about? • Numbers are expressed with a little subscript • 10010 vs. 1002

5. Converting from binary to decimal and back • 1 to 1 is easy, but what about 100? • Making a chart is the easiest method • 64, 32,16, 8, 4, 2, 1 • 1, 1, 0, 0, 1,0, 0 • 64+32+0+0+4+0+0 = 100 • 1100100

6. Back! • 1100 in binary is what in decimal? • 8, 4, 2, 1 • 8+4+0+0 • 12!

7. Binary Clock

8. Another Method • The “Chart” method works well both directions, but it can be time consuming. • The “division” method also works: • Lets try converting 12 to binary

9. 12/2 = ? R ? • 6 remainder 0 • So our rightmost number is a 0 • 6/2 = ? R ? • 3 remainder 0 • Our next number is a 0 • 3/2 = ? R ? • 1 remainder 1 • Our next number is a 1 • 1 / 2 = ? R ? • 0 remainder 1 • Our final number is a 1 • Collecting these numbers, we find that the number is 1100, which matches our earlier answer. It works!

10. Which to choose? • Either method works fine. • Choose which ever method you prefer.