This document provides examples of converting between binary and decimal number systems. It includes 10 binary to decimal conversions with step-by-step workings and 6 decimal to binary conversions shown systematically as repeated halvings until reaching 1. The goal is to practice these fundamental number system conversions through worked examples.

1. TALLER DE CONVERSIONES
DECIMAL A BINARIO Y BINARIO A DECIMAL
M. TÉCNICA EN SISTEMAS GRADO 10
SEPTIEMBRE DE 2014
INTEGRANTES:
Nombres y apellidos Yeison Arley Agudelo Mejia
Nombres y apellidos
1. CONVIERTA LOS SIGUIENTES NÚMEROS BINARIOS A DECIMAL. DEBE REALIZAR TODO EL PROCEDIMIENTO.
No. NÚMERO BINARIO RESPUESTA EN DECIMAL (PROCEMIENTO)
1 10001112 1x26 + 0x25 + 0x24 + 0x23 + 1x22 + 1x21 +1x20 = 64+0+0+0+4+2+1 = 7110
2 10000002 1x26 + 0x25 + 0x24 + 0x23 + 0x22 + 0x21 + 0x20 = 64+0+0+0+0+0+0 = 6410
3 11111112 1x26 + 1x25 + 1x24 + 1x23 + 1x22 + 1x21 + 1x20 = 64+32+16+8+4+2+1 = 12710
4 101010102 1x27 + 0x26 + 1x25 + 0x24 + 1x23 + 0x22 + 1x21 + 0x20 = 128+0+32+0+8+0+2+0 = 17010
5 110101012 1x27 + 1x26 + 0x25 + 1x24 + 0x23 + 1x22 + 0x21 + 1x20 =128+64+0+16+0+4+0+1= 21310
6 10001112 1x26 + 0x25 + 0x24 + 0x23 + 1x22 + 1x21 +1x20 = 64+0+0+0+4+2+1 = 7110
7 111111102
1x27 + 1x26 + 1x25 + 1x24 + 1x23 + 1x22 + 1x21 + 0x20 = 128+64+32+16+8+4+2+0 =
25410
8 1110000112
1x28 + 1x27 + 1x26 + 0x25 + 0x24 + 0x23 + 0x22 + 1x21 + 1x20 =
256+128+64+0+0+0+0+2+1 = 45110
9 101110002 1x27 + 0x26 + 1x25 + 1x24 + 1x23 + 0x22 + 0x21 + 0x20= 128+0+32+16+8+0+0+0= 18410
10 1100011102
1x28 + 1x27 + 0x26 + 0x25 + 0x24 + 1x23 + 1x22 + 1x21 + 0x20 =
256+128+0+0+0+8+4+2+0 = 39810

2. 2. CONVIERTA LOS SIGUIENTES NÚMEROS DECIMALES A BINARIO. DEBE REALIZAR TODO EL PROCEDIMIENTO.
No. NÚMERO DECIMAL RESPUESTA EN BINARIO (PROCEMIENTO)
1 15.60010
15600 2 = 0 15600 = 111100111100002
7800 2 = 0
3900 2 = 0
1950 2 = 0
975 2 = 1
487 2 = 1
243 2 = 1
121 2 = 1
60 2 = 0
30 2 = 0
15 2 = 1
7 2 = 1
3 2 = 1
1 2 = 1
0
2 10.80010
10800 2 = 0 10.800 = 101010001100002
5400 2 = 0
2700 2 = 0
1350 2 = 0
675 2 = 1
337 2 = 1
168 2 = 0
84 2 = 0
42 2 = 0
21 2 = 1
10 2 = 0
5 2 = 1
2 2 = 0
1 2 = 1
0

3. 3 11.79110
11791 2 = 1 11.791 = 10111000001111
5895 2 = 1
2947 2 = 1
1473 2 = 1
736 2 = 0
368 2 = 0
184 2 = 0
92 2 = 0
46 2 = 0
23 2 = 1
11 2 = 1
5 2 = 1
2 2 = 0
1 2 = 1
0
4 5.35910
5359 2 = 1 5.359 = 1010011101111
2679 2 = 1
1339 2 = 1
699 2 = 1
334 2 = 0
167 2 = 1
83 2 = 1
41 2 = 1
20 2 = 0
10 2 = 0
5 2 = 1
2 2 = 0
1 2 = 1
0
5 4.82510
4825 2 = 1 4825 = 1001011011001
2412 2 = 0
1206 2 = 0
603 2 = 1
301 2 = 1
150 2 = 0
75 2 = 1
37 2 = 1
18 2 = 0
9 2 = 1
4 2 = 0
2 2 = 0
1 2 = 1
0

4. 6 3.00010
3000 2 = 0 3000= 101110111000
1500 2 = 0
750 2 = 0
375 2 = 1
187 2 = 1
93 2 = 1
46 2 = 0
23 2 = 1
11 2 = 1
5 2 = 1
2 2 = 0
1 2 = 1
0
7 2.00010
2000 2 = 0 2000 = 11111010000
1000 2 = 0
500 2 = 0
250 2 = 0
125 2 = 1
62 2 = 0
31 2 = 1
15 2 = 1
7 2 = 1
3 2 = 1
1 2 = 1
0
8 1.56010
9 80010
800 2 = 0 800 = 1100100000
400 2 = 0
200 2 = 0
100 2 = 0
50 2 = 0
25 2 = 1
12 2 = 0
6 2 = 0
3 2 = 1
1 2 = 1
0
10 32910