University:
Boston University
Course:
CGS MA 121 | Calculus
Academic year:

2024
Views:

226

Pages:

9
Author:

Jerimiah Cantu

Binary “There are 10 types of people in the world… those that understand binary and those that don’t.” What is binary? • You and I write numbers like this: twelve is 12, sixty eight is 68, and one hundred is 100 • Binary is a number system that computers use. That is, binary is the way that computers express numbers. • It’s good to know binary because it helps us understand how computers think Base-10 • Our number system is made up of ten digits (0, 1, 2….9)….that’s why it’s called base-10. • We use those ten digits to express any number we want! • But how do we do this when there are only 10 of them? Base-10 Example 6 8 3 4 1000’s place 6 x 103 100’s place 8x 102 10’s place 3x 101 1’s place 4 x 100 So the number 6834 is made up of six 1000s, eight 100s, three 10s, and four 1s. In other words… 6834 = (6 x 1000) + (8 x 100) + (3 x 10) + (4 x 1) Places • What are the first few places in our number system? – Ones, tens, hundreds, thousands, ten thousands, hundred thousands, millions, etc… • Do you notice any patterns here? • Each one is ten times bigger than the one before it! What is binary? • • • • Binary is just like our number system…. Except it only uses two digits! The only digits in binary are 0 and 1 In base-10 (the normal number system), any number bigger than 9 needs more than one digit. • In binary, any number bigger than 1 needs more than one digit. Exponents in Binary • There are ten possible digits in the Base-10 number system (0 to 9). • Powers of 10 are used to decide the places values. • If binary only has two possible digits, what do you think is used to decide the values of its places? • Powers of 2!  Binary Example System 1 0 1 0 8’s place 1 x 23 4’s place 2’s place 22 21 0x 1x What is 1010 equal to in the base-10 number system? 1’s place 0 x 20 So the number 1010 in BINARY is made up of one 8, zero 4s, one 2, and zero 1s. 1010 is binary for (1 x 8) + (0 x 4) + (1 x 2) + (0 x 1) Let’s Count! …in Base-10 …in Binary 0 1 2 3 4 5 6 7 8 9 10 0 1 10 11 100 101 110 111 1000 1001 1010 Are there any patterns that you notice?

What Is Binary Lecture Note

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