# SCEN103 10/22 Class

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### Being Digital: Counting

"Not everything that counts can be counted, and not everything that can be counted counts." -- Albert Einstein

#### Today's Class

• "Relearning" to count
• Preparation for study of digital electronics
• 1 + 11 = 100 ?

• Review of decimal scheme -- most familiar
• "Place holders" are powers of 10
The following powers of 10: 3, 2, 1, 0
correspond to "weights" of 1000, 100, 10, 1
• Ten symbols or characters needed:
0, 1, 2, 3, 4, 5, 6, 7, 8, and 9

• Introduction to binary counting -- base 2
• Motivation -- only 2 states needed:
-- Switch ON or OFF,
-- Circuit CLOSED or OPEN,
-- Current FLOWING or NOT,
-- Voltage HIGH or LOW
• Place holders are powers of 2
 Power of 2 Weight 7 6 5 4 3 2 1 0 128 64 32 16 8 4 2 1
• Example: convert 1100011 to decimal
• Correspondence between decimal digit and binary bits
-- "bit" is a contraction of "binary digit"

Decimal Binary
0 0000
1 0001
2 0010
3 0011
4 0100
5 0101
6 0110
7 0111
8 1000
9 1001

• Can 1 + 11 = 100?

• Hexadecimal numbers -- hex for short
• Binary numbers can be unwieldy in length
• Place holders are powers of 16
 Power of 16 Weight 3 2 1 0 4096 256 16 1
• Sixteen symbols or characters needed:
The usual 10 of 0, 1, 2, ... 9 plus A, B, C, D, E, and F
• Correspondence between new hexadecimal digits and decimal/binary
Decimal Hex Binary
10 A 1010
11 B 1011
12 C 1100
13 D 1101
14 E 1110
15 F 1111
• 4 bits used to represent a single hex digit
• Example: conversion of 7CC to decimal, to binary

• Addition of two binary numbers
• Need to know that
1+0=1 -- no surprise
1+1=10 -- don't forget to carry!
1+1+1=11
• Example: B+E=?

#### Group Activity

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