How many outputs does a BCD (4-to-10) decoder have, and what does it activate?

10 outputs, one for each decimal digit

How is the end carry treated in 1's versus 2's complement subtraction?

1's complement adds it back (end-around); 2's complement discards it

1's complement discards it; 2's adds it back

2075 Asoj · 3+3 marks

BCD decoder; 1's and 2's complements

Short answer

BCD decoder activates one of ten outputs: D0=A'B'C'D', D1=A'B'C'D, D2=B'CD', D3=B'CD, D4=BC'D', D5=BC'D, D6=BCD', D7=BCD, D8=AD', D9=AD. 1's complement inverts all bits; 2's complement adds 1 to the 1's complement.

Realize the circuit diagram for BCD decoder. Explain 1's and 2's complements with examples?

BCD decoder (BCD-to-decimal, 4-to-10)

A BCD decoder takes a 4-bit BCD code $ABCD$ ( $A$ = MSB) and activates one of ten outputs $D_0$ – $D_9$ (IC 7442). Codes 1010–1111 never occur, so they are don't-cares and allow partial decoding.

Digit	ABCD	Full decoding	Simplified (with don't-cares)
0	0000	$A'B'C'D'$	$A'B'C'D'$
1	0001	$A'B'C'D$	$A'B'C'D$
2	0010	$A'B'CD'$	$B'CD'$
3	0011	$A'B'CD$	$B'CD$
4	0100	$A'BC'D'$	$BC'D'$
5	0101	$A'BC'D$	$BC'D$
6	0110	$A'BCD'$	$BCD'$
7	0111	$A'BCD$	$BCD$
8	1000	$AB'C'D'$	$AD'$
9	1001	$AB'C'D$	$AD$

 A B C D   A' B' C' D'  (inverters)
 |  |  |  |
 +--+--+--+--[AND]--- D0 = A'B'C'D'
 +--+--+--+--[AND]--- D1 = A'B'C'D
      ...  (one AND gate per output)
 +--------+--[AND]--- D8 = AD'
 +--------+--[AND]--- D9 = AD

Ten AND gates and four inverters form the decoder.

1's and 2's complements

1's complement: invert every bit (0 → 1, 1 → 0). Example: 1's complement of $10110$ is $01001$ .

2's complement: 1's complement + 1. Example: 2's complement of $10110$ is $01001 + 1 = 01010$ .

They represent negative numbers and turn subtraction into addition. Example $9 - 5$ in 4 bits:

 1's complement method        2's complement method
   1001  (9)                    1001  (9)
 + 1010  (1's comp of 0101)   + 1011  (2's comp of 0101)
 ------                       ------
 1 0011                       1 0100
     +1  end-around carry      carry discarded
 ------                       
   0100  = 4                    0100  = 4

In 1's complement the end carry is added back; in 2's complement it is discarded. 2's complement has a single zero and is used in computers.

✓ Answer checked by Claude Opus 5.5 (high effort)

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