Lab: Decimal, Binary, Hexadecimal Numbering Systems
ITEC3831
Name: ______
Lab: Decimal, Binary, Hexadecimal Numbering Systems
1. Basic number conversion table:
Decimal / 15 / 14 / 13 / 12 / 11 / 10 / 9 / 8 / 7 / 6 / 5 / 4 / 3 / 2 / 1 / 0Hex / F / E / D / C / B / A / 9 / 8 / 7 / 6 / 5 / 4 / 3 / 2 / 1 / 0
Binary / 1111 / 1110 / 1101 / 1100 / 1011 / 1010 / 1001 / 1000 / 111 / 110 / 101 / 100 / 11 / 10 / 1 / 0
2. Example of Decimal, Binary, Hexadecimal Numbers
… / 3 / 2 / 1 / 0… / 103=1000 / 102=100 / 101=10 / 100=1
… / 0 / 2 / 2 / 6
Decimal: Base 10
Example: 226
… / 7 / 6 / 5 / 4 / 3 / 2 / 1 / 0… / 27=128 / 26=64 / 25=32 / 24=16 / 23=8 / 22=4 / 21=2 / 20=1
… / 1 / 1 / 1 / 0 / 0 / 0 / 1 / 0
Binary: Base 2
Example: 11100010
… / 3 / 2 / 1 / 0… / 163=4096 / 162=256 / 161=16 / 160=1
… / 0 / 0 / E / 2
Hex: Base 16
Example: 0xE2
3. Going from Binary/ Hexadecimal to Decimal:
… / 7 / 6 / 5 / 4 / 3 / 2 / 1 / 0… / 27=128 / 26=64 / 25=32 / 24=16 / 23=8 / 22=4 / 21=2 / 20=1
… / 1 / 1 / 1 / 0 / 0 / 0 / 1 / 0
Binary to Decimal:
Example: 11100010
Solution:
=1x27 + 1x26 + 1x25 + 0x24 + 0x23 + 0x22 + 1x21 + 0x20
=1x128 + 1x64 + 1x32 + 0x16 + 0x8 + 0x4 + 1x2 + 0x1
=128 + 64 + 32 + 0 + 0 + 0 + 2 + 0
=226
… / 3 / 2 / 1 / 0… / 163=4096 / 162=256 / 161=16 / 160=1
… / 0 / 0 / E / 2
Hexadecimal to Decimal:
Example: 0xE2
Solution:
=0x163 + 0x162 + Ex161 + 2x160
=0x4096 + 0x256 + 14x16 + 2x1
=0 + 0 + 224 + 2
=226
4. Going from Decimal to Binary/ Hexadecimal:
Example:
Decimal: 123 to Binary
Steps:
1. Find the closest 2 to the power of x
2. If (123 ≥ 27) the 7th position: 1, else: 0 123-0x27 = 123
… / 7 / 6 / 5 / 4 / 3 / 2 / 1 / 0… / 27=128 / 26=64 / 25=32 / 24=16 / 23=8 / 22=4 / 21=2 / 20=1
… / 0 / 1 / 1 / 1 / 1 / 0 / 1 / 1
3. If (123≥26) the 6th position: 1, else: 0 123 – 1x26= 59
4. If (59 ≥ 25) the 5th position: 1, else: 0 59 - 1x 25 = 27
5. If (27 ≥ 24) the 4th position: 1, else: 0 27 - 1x 24 = 11
6. If (11 ≥ 23) the 3rd position: 1, else: 0 11 - 1x 23 = 3
7. If (3 ≥ 22) the 2nd position: 1, else: 0 3 - 0x 22 = 3
8. If (3 ≥ 21) the 1st position: 1, else: 0 3 - 1x 21 = 1
8. If (1 ≥ 20) the 0th position: 1, else: 0 1 - 1x 20 = 0
Example:
Decimal: 3257 to Hexadecimal
Steps:
1. Find the closest 16 to the power of x
2. 3257 163, then the 3rd position: 0
3. 3257 ≥ 162
3257 ÷ 162 = 12.72xxx , so the 2nd position: 0xC
3257 – 12x162 = 185
4. 185 161)
185 ÷ 161 = 11.5625 , so the 1st position: 0xB
185 – 11x161 = 9
5. 9 ≥ 20
… / 3 / 2 / 1 / 0… / 163=4096 / 162=256 / 161=16 / 160=1
… / 0 / C / B / 9
9÷ 160 = 9 , so the 0th position: 0x9
9– 9x160 = 0
5. Going from Binary to Hex and back
Binary to Hex: 11010010
Steps:
1101 / 00101. Group digits, from right to left 4digits one group.
2. Convert each group to Hex,
From the Basic number conversion table: 1101 = 0xD; 0010= 0x2
3. The final result: 0xD2
Hex to Binary: 0x3C
Steps:
From the Basic number conversion table:
0x3 = 0011; 0xC= 1100
3. The final result: 00111100
6. In Class Lab:
1. Take the following decimal numbers and convert them to binary and hexadecimal:
a) 20
Binary: ______Hexadecimal: ______
b) 35
Binary: ______Hexadecimal: ______
c) 127
Binary: ______Hexadecimal: ______
d) 93
Binary: ______Hexadecimal: ______
2. Take the following binary numbers and convert to hex and decimal:
a) 011101
Decimal: ______Hexadecimal: ______
b) 0110
Decimal: ______Hexadecimal: ______
c) 1010101
Decimal: ______Hexadecimal: ______
3. Take the following hex numbers and convert to binary and decimal:
a) 1F
Decimal: ______Binary: ______
b) FE
Decimal: ______Binary: ______
c) A23
Decimal: ______Binary: ______