MATH 1100 notes Test 2 COUNTING ON FINGERS: Counting on Fingers Begin by labeling your fingers as follows. The individual fingers show the powers of 2. Two show the number 3, hold up the fingers labeled 1 and 2 together. Use your fingers to “show” the numbers 1, 2, 3, 4, . .., all the way to 27. [Note: When you show the numbers 4 and 128, be prepared to close your fist right away!] To show 3 on our fingers, we use the pinkie finger and the ring finger of our right hand. The pinkie finger on the left hand represents 512. All ten fingers together represent 512+256+128+64+32+16+8+4+2+1. How much is that? Instead of doing the addition, imagine that we had an eleventh finger, which would represent 1024 (this is twice 512, the value of the tenth finger). The number represented by all ten fingers up is the number that comes right before 1024, so it is 1023. BINARY NOTATION Numbers Written in Binary (= base 2) Begin by labeling your fingers as follows. The individual fingers show the powers of 2. To show the number 3, hold up the fingers labeled 1 and 2 together. Use your fingers to “show” the numbers 1, 2, 3, 4, . .., all the way to 27. Then you’ll understand binary. [Note: When you show the numbers 4 and 128, be prepared to close your fist right away!] To show 3 on our fingers in binary, we use the pinkie finger and the ring finger of our right hand. To write 3 in binary, we indicate those two fingers by writing 11_ bin . The 11 is read “one-one” and NOT “eleven” . The subscript bin written small reminds us that we are using binary and not using “base ten” numerals. Example: 101_ bin is binary notation for the number 1x2 2 + 0x2 1 + 1x2 0 = 4+1 = 5. The coefficients are only 0 or 1, indicating that the corresponding finger in the picture of hands are raised (“1”) or not raised (“0”).

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Using all ten fingers, the pinkie on the left hand represents 512. All ten fingers together represent 512+256+128+64+32+16+8+4+2+1. How much is that? Instead of doing the addition, imagine that we had an eleventh finger, which would represent 1024 (this is twice the value of the tenth finger). The number represented by all ten fingers up is the number that comes right before 1024, so it is 1023. Using binary notation, we can “count” from 1 to 1023 using our ten fingers. That’s a whole lot more than we can count in base ten! Example. Have a friend think of a number from 1 to 15. How many “yes/no” questions do we need to ask in order to discover her number? The first power of 2 greater than 15 is 16=2 4 . Make four blanks: ___ ___ ___ ___ which we will fill in with 0’s and 1’s to create a number written in binary. The algorithm (= method) we use to discover our friend’s number is called “Divide and

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This note was uploaded on 10/11/2011 for the course PSYC, PSYC 2076, 2060 taught by Professor Briganti,gustan,perlis,namikas,wheeler during the Spring '10 term at LSU.