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Sawel Keay & Jonathan Tanious
Ms. Alamparambil
Math 304
Monday, October 3, 2022
“Binary And Hexadecimal Number Systems”
Script: Sawel Jonathan
Intro:
Technology has changed our lives dramatically over the years, especially this past
decade. It has significantly evolved to serve our needs in every facet of our lives; navigation,
communication, education, calculations, finance, everything can be done using a device. Has it
ever occurred to you, how do they do it? How are they able to do all these things simultaneously
in a split second? It all starts with a number system that dates all the way back to Ancient Egypt,
known as Binary.
Origin of Binary:
As previously mentioned, the binary number system was first used by the Ancient
Egyptians thousands of years ago. However, it was lost and at that time a German mathematician
named Gottfried Leibniz invented binary. He saw it as a way to express language in numbers
using ones and zeros. For example, “Hi” in binary would be 1001000 and 1101001. In basic
terms, binary is a way to base ten numbers in base 2.
, 2
Origin of Hexadecimal:
A number system closely related to binary is the hexadecimal number system which was
much more recently invented by John W. Nystrom in 1859 in France at age 34. The purpose of
this number system was to make binary lines more concise and understandable for us humans.
The Relationship Between Base 10 Number system to These Ones:
Base 10:
The number system we use in math is in base 10 meaning it is represented in powers of
ten like our place value chart which consists of ones, tens, hundreds, thousands and so on. To see
the relationship between these number systems we will use 19. So, we would represent the
number 19 as one ten and nine ones.
Decimal->Binary:
So to convert base 10 to binary or base 2, we use the powers of two to represent the
decimal value using this chart. Instead of writing the powers of ten, from right to left starting at
10 to the power of 0 and so on, we use powers of 2 in this fashion. We see what is the largest
power of two that fits the number we are converting and put a one under that power in our chart.
From there, you would subtract that power of two from the number we are converting and see
Sawel Keay & Jonathan Tanious
Ms. Alamparambil
Math 304
Monday, October 3, 2022
“Binary And Hexadecimal Number Systems”
Script: Sawel Jonathan
Intro:
Technology has changed our lives dramatically over the years, especially this past
decade. It has significantly evolved to serve our needs in every facet of our lives; navigation,
communication, education, calculations, finance, everything can be done using a device. Has it
ever occurred to you, how do they do it? How are they able to do all these things simultaneously
in a split second? It all starts with a number system that dates all the way back to Ancient Egypt,
known as Binary.
Origin of Binary:
As previously mentioned, the binary number system was first used by the Ancient
Egyptians thousands of years ago. However, it was lost and at that time a German mathematician
named Gottfried Leibniz invented binary. He saw it as a way to express language in numbers
using ones and zeros. For example, “Hi” in binary would be 1001000 and 1101001. In basic
terms, binary is a way to base ten numbers in base 2.
, 2
Origin of Hexadecimal:
A number system closely related to binary is the hexadecimal number system which was
much more recently invented by John W. Nystrom in 1859 in France at age 34. The purpose of
this number system was to make binary lines more concise and understandable for us humans.
The Relationship Between Base 10 Number system to These Ones:
Base 10:
The number system we use in math is in base 10 meaning it is represented in powers of
ten like our place value chart which consists of ones, tens, hundreds, thousands and so on. To see
the relationship between these number systems we will use 19. So, we would represent the
number 19 as one ten and nine ones.
Decimal->Binary:
So to convert base 10 to binary or base 2, we use the powers of two to represent the
decimal value using this chart. Instead of writing the powers of ten, from right to left starting at
10 to the power of 0 and so on, we use powers of 2 in this fashion. We see what is the largest
power of two that fits the number we are converting and put a one under that power in our chart.
From there, you would subtract that power of two from the number we are converting and see
