《数字电》英文版 chapter2-2 Boolean switching algebra

服器 Boolean switching algebra Chapter 2 Karnaugh maps

Boolean switching algebra Chapter 2 Karnaugh maps

MSB B SB- 0011110 5 CD200011110 00 01 11 3 4576 2354 0 10 MSB=A. LSB=D

00 01 11 10 0 1 0 1 2 3 6 7 4 5 AB C MSB LSB 00 01 11 10 AB CD 00 01 11 10 0 4 12 8 1 5 13 9 3 7 15 11 2 6 14 10 MSB=A ; LSB=D

ABC DE 000001011010 0004128 0115139 ABC 371511 DE 100101111110 102614 10 0016202824 MSB=A. LSB=E 0117212925 19233127 1018223026 MSB=A, LSB=E

000 001 011 010 ABC DE 00 01 11 10 0 4 12 8 1 5 13 9 3 7 15 11 2 6 14 10 MSB=A ; LSB=E 100 101 111 110 ABC DE 00 01 11 10 16 20 28 24 17 21 29 25 19 23 31 27 18 22 30 26 MSB=A ; LSB=E

RIt is a matrix of squares. each square represent a minterm or maxterm from a Boolean equation R N-variable karnaugh map have 2n squares. R The binary numeral on the sides of k-map is the variable coordinates

It is a matrix of squares. each square represent a minterm or maxterm from a Boolean equation. N-variable karnaugh map have 2n squares. The binary numeral on the sides of k-map is the variable coordinates

R By decoding the binary coordinates, We label the decimal value for each square MSB 圆 The decimal number is LSB- 00011110 the subscript of the 0 relative minterm or maxterm 圆50 a direct connection .00011110 can be made between 04 28 00 the minterm or maxterm 153 equation list and the 01 appropriate square in karna h map g 26140 10 MSB=A. LSB=D

By decoding the binary coordinates, We label the decimal value for each square. 00 01 11 10 0 1 0 1 2 3 6 7 4 5 AB C MSB LSB The decimal number is the subscript of the relative minterm or maxterm. So a direct connection can be made between the minterm or maxterm equation list and the appropriate square in karnaugh map. 00 01 11 10 AB CD 00 01 11 10 0 4 12 8 1 5 13 9 3 7 15 11 2 6 14 10 MSB=A ; LSB=D

R: The squares correspond to the adjacent minterms are ad jacent squares Across the top and down the side of k-map, only one bit changes occur between ad jacent squares for each column and row 8: Logically adjacent 2 Adjacent C 00011110 04 28 Symmetrica 00 (0,8,24) 01 37 (13911) 51 26 410 o stack 10 MSB=A. LSB=D

The squares correspond to the adjacent minterms are adjacent squares. Across the top and down the side of k- map, only one bit changes occur between adjacent squares for each column and row Logically adjacent Adjacent Symmetrical (0,8,2,4) (1,3,9,11) stack 00 01 11 10 AB CD 00 01 11 10 0 4 12 8 1 5 13 9 3 7 15 11 2 6 14 10 MSB=A ; LSB=D

Describe a switching function K-map

Describe a switching function by K-map

F(ABCD)n(13512131415 CD00011110 图 Writing l in Th 28 00 square correspond 53 To a rrnrerrn 01 715 2614Ah0 10 MSB=A: LSB=D

F(A,B,C,D)=∑m(1,3,5,12,13,14,15) 00 01 11 10 AB CD 00 01 11 10 0 4 12 8 1 5 13 9 3 7 15 11 2 6 14 10 MSB=A ; LSB=D 1 1 1 1 1 1 1 Writing 1 in the square correspond to a minterm

剧F(ABCD)M(235710,111415) 0001110 图 Writing o in the 0 00 square correspond 139 01 50 o a axerol 1183070151 0 10 0 00 0 MSB=A. LSB=D

F(A,B,C,D)=∏M(2,3,5,7,10,11,14,15) 00 01 11 10 AB CD 00 01 11 10 0 4 12 8 1 5 13 9 3 7 15 11 2 6 14 10 MSB=A ; LSB=D 0 0 0 0 0 0 0 0 Writing 0 in the square correspond to a maxterm

Simplify a equation use N-Variable K-map

Simplify a equation use N-variable K-map