Number Converesions

Number Conversions

Binary Numbers

The decimal counting system uses the Base-10 numbering system where
each digit in a number takes on one of ten possible values, called “digits”,
from 0 to 9, eg. 21310 (Two Hundred and Thirteen).

Binary & Decimal Numbers

Binary Numbering System is the most fundamental numbering
system in all digital and computer based systems

The binary numbering system works on powers of two giving a
binary to decimal conversion from base-2 to base-10.

Each “0” and “1” is considered to be a single binary digit (bit)

01

02

03

04

Representation of a Binary Number

Right-hand most bit being the Least Significant Bit or LSB,
Left-hand most bit being the Most

Significant Bit or MSB

Binary Number Names & Prefixes

SLIDESMANIA.COM

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A “bit” is the abbreviated term derived from BInary digit

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A Binary system has only two states, Logic “0” and Logic “1” giving a

base of 2

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A Decimal system uses 10 different digits, 0 to 9 giving it a base of 10

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A Binary number is a weighted number who’s weighted value increases

from right to left

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The weight of a binary digit doubles from right to left

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A decimal number can be converted to a binary number by using the

sum-of-weights method or the repeated division-by-2 method

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When we convert numbers from binary to decimal, or decimal to binary,

subscripts are used to avoid errors

Binary to Decimal Summary

Converting Binary -> Decimal

0010 1110 =

0001 1001 =

Converting Decimal -> Binary

33 =

153 =

220 =

Hexadecimal Numbers

The one main disadvantage of binary numbers is that the binary string
equivalent of a large decimal base-10 number can be quite long. One way
of overcoming this problem is to group the binary numbers into sets of
four bits. These groups of 4-bits uses another type of numbering system
called Hexadecimal Numbers.

Hexadecimal Numbers

The “Hexadecimal” or simply “Hex” numbering system uses Base 16.

Hex uses 16 different symbols to represent the numbers 0-15. The
symbols are the numbers 0-9 then capital letters of A, B, C, D, E and F

Hex is mainly used when dealing with computers and memory
address locations or representing RGB Color

01

02

03

04

https://www.electronics-tutorials.ws/binary/bin_3.html

0…to…9, A,B,C,D,E,F, 10…to…19, 1A, 1B, 1C, 1D, 1E, 1F, 20, 21….etc

Counting using Hexadecimal Numbers

Do not get confused, 10 or 20 is NOT ten or twenty it is 1 + 0 and 2 + 0 in
hexadecimal. With two hexadecimal numbers, we can count up to FF which is
equal to decimal 255. Likewise, to count higher than FF we would add a third
hexadecimal digit to the left so the first 3-bit hexadecimal number would be 10016,
(25610) and the last would be FFF16, (409510).

D216=

9116=

​Converting Hex -> Decimal

Converting Decimal -> Hex

2010=

18210=

Multiple Choice

Convert 85₁₀ into Hexadecimal

• 01010101
• 55
• 5A
• A5

Converting Hex -> Binary

A716 =

5016=

Multiple Choice

What is the binary equivalent of 4A₁₆

• 1010 0100

• 0100 1010

• 0011 0010

• 1000 1100

Converting Binary -> Hex

1110 10102=

1101 01112 =

Multiple Choice

What is the Hex equivalent for 1001 0011₂

• 93

• 12

• C

• 147

Multiple Choice

A video game character can face toward one of four directions: north, south, east, and west. Each direction is stored in memory as a sequence of four bits. A new version of the game is created in which the character can face toward one of eight directions, adding northwest, northeast, southwest, and southeast to the original four possibilities. Which of the following statements is true about how the eight directions must be stored in memory?

• Four bits are not enough to store the eight directions. Five bits are needed for the new version of the game.

• Four bits are not enough to store the eight directions. Eight bits are needed for the new version of the game.

• Four bits are not enough to store the eight directions. Sixteen bits are needed for the new version of the game.

• Four bits are enough to store the eight directions.

Multiple Choice

Why do Computers use Binary Numbers Instead of Decimal Numbers?

• Because Computers just do.

• Computers use binary numbers to store data.

• The digits 1 and 0 used in binary reflect the off and on states of a transistor.

• Because Decimals are too easy

Multiple Choice

What is one of the primary benefits of using hexadecimal numbers in computing?

• Hexadecimal numbers are easier for humans to read and write than binary numbers.

• Hexadecimal numbers use fewer digits than decimal numbers for the same value.

• Hexadecimal numbers are universally accepted in all programming languages.

• Hexadecimal numbers can represent a larger range of values than octal numbers.

Unit Conversions