- "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

- "Place holders" are powers of 10
- 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 7 6 5 4 3 2 1 0 Weight 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?

- Motivation -- only 2 states needed:
**Hexadecimal numbers**-- hex for short- Binary numbers can be unwieldy in length
- Place holders are powers of 16

Power of 16 3 2 1 0 Weight 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=?

- Need to know that

- Find the sum of BAD and 1CE by adding their binary equivalents.

Report as a hexadecimal number. - Check your answer using decimal arithmetic.
**Solution**

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Comments, suggestions, or requests to ghw@udel.edu.

"http://www.physics.udel.edu/~watson/scen103/clas1022.html"

Last updated Oct. 22, 1996.

Copyright George Watson, Univ. of Delaware, 1996.