Example: Binary to Octal

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Example Binary to Octal

725.23 111 010 101 .
010 011
111010101.010011
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Binary to Hexadecimal
2EB9.C
2 E B 9 . C
0010 1110 1011 1001 . 1100
0010111010111001.1100
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Complements
In (R-1) Individually complement each
digit Examples base 10 90320 goes to 09679
base 2 10011 goes to 01100
base 4 32012 goes to 01321 In (R)Ignore
LSBs of zero(s) complement first non-zero digit
with (R-1) complement the rest with
(R) Examples base 10 90320 goes to 09680
base 2 10011 goes to 01101
base 4 32012 goes to 01322
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Subtraction (2s complement)
Solving for (M - N), where M 10010110 (and
M 01101010) N 01110100 (and N
10001100) (M - N) 10010110 (M) (N - M)
01110100 (N) 10001100 (N)
01101010 (M)
100100010
011011110 carry means ()
no carry means (-) answer 00100010
answer 11011110
answer (-)00100010
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Subtraction (1s complement)
M 10010110 (and M 01101001) N
01110100 (and N 10001010 (M - N)
(N - M) 10010110
(M) 01110100 (N) 10001011 (N)
01101001 (M) 100100001
011011101 1
11011101 00100010 (M - N) (-)
00100010 (-) (M- N)
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Signed Binary Numbers
Signed Magnitude ()5 (-)6 In binary
Convention is to use left bit 0 for () 1 for
(-) Example 10000110 is (-)6 Better to use
Signed Complement (say 2s complement) Steps
to accomplish 1. Express as a positive number
0000 1101 () 13 2. Take 2s complement
11110011 (-) 13
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Addition signed binary
Put negative numbers into 2s complement Add
numbers together Disregard any carry out If
answer has a 1 in the left bit, the answer is
negative (-) and you must then complement it
(sign bit and all) Example ()3 (-)7
(-)4 0000 0011 2s complement of 7 . . .
1111 1001 1111 1100 Left bit is a 1 so you
know answer is negative Take 2s complement
for answer (-) 000 0100, or (-)4

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Subtraction in signed binary

• Express all negative numbers in 2s complement
• Take 2s complement of the subtrahend
• Add the two numbers together
• Discard any carry over
• If left bit is a 0 the answer is positive
• If left bit is a 1 the answer is negative and
  you must take the 2s complement to get the
  answer
• Example (-)7 - (-)9 1111 1001 - 1111
  0111
• 1111 1001 0000 1001 1 0000 0010 ()2

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Subtraction (contd)
Now try this (-)9 - (-)7. . . And answer
better be (-)2 1111 0111 - 1111 1001 . . .
Take 2s complement of subtrahend 1111 0111
0000 0111 1111 1110 answer has a 1 in
its left bit therefore its negative take 2s
complement 0000 0010 and get (-) 2 as the
answer
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Binary Codes

• BCD
• Excess-3 84-2-1 2421 (self complementing)
• Error Detection Codes (parity)
• Gray Code
• ASCII Code
• Hollarith Code
• EBCDIC.

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Binary Storage and Registers

• Registers
• Register transfer
• Discuss Fig. 1-2
• Discuss Fig. 1-2

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Binary Logic

• AND, OR, NOT
• Truth Tables
• Switching Circuits
• Gates
• Thresholds
• Multiple inputs
• Timing Diagrams

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Laboratory Comments

• Volts, amps, ohms, watts
• VOM
• resister codes
• wire sizes
• breadboard
• equipment function generators, oscilloscopes,
  etc
• test probes
• report writing